diff --git a/poetry.lock b/poetry.lock
index e860023..1acac5e 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -176,13 +176,13 @@ tests-no-zope = ["attrs[tests-mypy]", "cloudpickle", "hypothesis", "pympler", "p
 
 [[package]]
 name = "babel"
-version = "2.14.0"
+version = "2.15.0"
 description = "Internationalization utilities"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
 files = [
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-    {file = "Babel-2.14.0.tar.gz", hash = "sha256:6919867db036398ba21eb5c7a0f6b28ab8cbc3ae7a73a44ebe34ae74a4e7d363"},
+    {file = "Babel-2.15.0-py3-none-any.whl", hash = "sha256:08706bdad8d0a3413266ab61bd6c34d0c28d6e1e7badf40a2cebe67644e2e1fb"},
+    {file = "babel-2.15.0.tar.gz", hash = "sha256:8daf0e265d05768bc6c7a314cf1321e9a123afc328cc635c18622a2f30a04413"},
 ]
 
 [package.extras]
@@ -211,33 +211,33 @@ lxml = ["lxml"]
 
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 name = "black"
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+version = "24.4.2"
 description = "The uncompromising code formatter."
 optional = false
 python-versions = ">=3.8"
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 [package.dependencies]
@@ -979,13 +979,13 @@ testing = ["Django", "attrs", "colorama", "docopt", "pytest (<7.0.0)"]
 
 [[package]]
 name = "jinja2"
-version = "3.1.3"
+version = "3.1.4"
 description = "A very fast and expressive template engine."
 optional = false
 python-versions = ">=3.7"
 files = [
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 ]
 
 [package.dependencies]
@@ -1018,13 +1018,13 @@ files = [
 
 [[package]]
 name = "jsonschema"
-version = "4.21.1"
+version = "4.22.0"
 description = "An implementation of JSON Schema validation for Python"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -1243,13 +1243,13 @@ test = ["jupyter-server (>=2.0.0)", "pytest (>=7.0)", "pytest-jupyter[server] (>
 
 [[package]]
 name = "jupyterlab"
-version = "4.1.6"
+version = "4.1.8"
 description = "JupyterLab computational environment"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -1261,7 +1261,7 @@ jinja2 = ">=3.0.3"
 jupyter-core = "*"
 jupyter-lsp = ">=2.0.0"
 jupyter-server = ">=2.4.0,<3"
-jupyterlab-server = ">=2.19.0,<3"
+jupyterlab-server = ">=2.27.1,<3"
 notebook-shim = ">=0.2"
 packaging = "*"
 tomli = {version = ">=1.2.2", markers = "python_version < \"3.11\""}
@@ -1288,13 +1288,13 @@ files = [
 
 [[package]]
 name = "jupyterlab-server"
-version = "2.26.0"
+version = "2.27.1"
 description = "A set of server components for JupyterLab and JupyterLab like applications."
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -1467,38 +1467,38 @@ dev = ["absl-py", "pyink", "pylint (>=2.6.0)", "pytest", "pytest-xdist"]
 
 [[package]]
 name = "mypy"
-version = "1.9.0"
+version = "1.10.0"
 description = "Optional static typing for Python"
 optional = false
 python-versions = ">=3.8"
 files = [
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@@ -1547,13 +1547,13 @@ test = ["flaky", "ipykernel (>=6.19.3)", "ipython", "ipywidgets", "nbconvert (>=
 
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@@ -1575,9 +1575,9 @@ tinycss2 = "*"
 traitlets = ">=5.1"
 
 [package.extras]
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 serve = ["tornado (>=6.1)"]
 test = ["flaky", "ipykernel", "ipywidgets (>=7.5)", "pytest (>=7)"]
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 [[package]]
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 [package.extras]
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-test = ["flake8", "isort", "pytest"]
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 [[package]]
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-    {file = "websocket-client-1.7.0.tar.gz", hash = "sha256:10e511ea3a8c744631d3bd77e61eb17ed09304c413ad42cf6ddfa4c7787e8fe6"},
-    {file = "websocket_client-1.7.0-py3-none-any.whl", hash = "sha256:f4c3d22fec12a2461427a29957ff07d35098ee2d976d3ba244e688b8b4057588"},
+    {file = "websocket_client-1.8.0-py3-none-any.whl", hash = "sha256:17b44cc997f5c498e809b22cdf2d9c7a9e71c02c8cc2b6c56e7c2d1239bfa526"},
+    {file = "websocket_client-1.8.0.tar.gz", hash = "sha256:3239df9f44da632f96012472805d40a23281a991027ce11d2f45a6f24ac4c3da"},
 ]
 
 [package.extras]
-docs = ["Sphinx (>=6.0)", "sphinx-rtd-theme (>=1.1.0)"]
+docs = ["Sphinx (>=6.0)", "myst-parser (>=2.0.0)", "sphinx-rtd-theme (>=1.1.0)"]
 optional = ["python-socks", "wsaccel"]
 test = ["websockets"]
 
diff --git a/pyproject.toml b/pyproject.toml
index 0320053..7ceb644 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "variPEPS"
-version = "0.5.5"
+version = "0.6.0"
 description = "Versatile tensor network library for variational ground state simulations in two spatial dimensions"
 authors = ["Jan Naumann <j.naumann@fu-berlin.de>", "Philipp Schmoll <philipp.schmoll@fu-berlin.de>", "Frederik Wilde", "Finn Krein"]
 license = "GPL-3.0-or-later"
diff --git a/varipeps/contractions/definitions.py b/varipeps/contractions/definitions.py
index 0e2ba41..7ccd5a0 100644
--- a/varipeps/contractions/definitions.py
+++ b/varipeps/contractions/definitions.py
@@ -195,6 +195,254 @@ def _prepare_defs(cls):
         ],
     }
 
+    density_matrix_one_site_C1_phase: Definition = {
+        "tensors": [
+            [
+                "tensor",
+                "tensor_conj",
+                "C1_phase",
+                "T1",
+                "C2",
+                "T2",
+                "C3",
+                "T3",
+                "C4",
+                "T4",
+            ]
+        ],
+        "network": [
+            [
+                (6, 7, -1, 10, 9),  # tensor
+                (13, 14, -2, 15, 16),  # tensor_conj
+                (2, 12),  # C1_phase
+                (12, 9, 16, 3),  # T1
+                (3, 8),  # C2
+                (10, 15, 4, 8),  # T2
+                (11, 4),  # C3
+                (1, 11, 14, 7),  # T3
+                (1, 5),  # C4
+                (5, 13, 6, 2),  # T4
+            ]
+        ],
+    }
+
+    density_matrix_one_site_C2_phase: Definition = {
+        "tensors": [
+            [
+                "tensor",
+                "tensor_conj",
+                "C1",
+                "T1",
+                "C2_phase",
+                "T2",
+                "C3",
+                "T3",
+                "C4",
+                "T4",
+            ]
+        ],
+        "network": [
+            [
+                (6, 7, -1, 10, 9),  # tensor
+                (13, 14, -2, 15, 16),  # tensor_conj
+                (2, 12),  # C1
+                (12, 9, 16, 3),  # T1
+                (3, 8),  # C2_phase
+                (10, 15, 4, 8),  # T2
+                (11, 4),  # C3
+                (1, 11, 14, 7),  # T3
+                (1, 5),  # C4
+                (5, 13, 6, 2),  # T4
+            ]
+        ],
+    }
+
+    density_matrix_one_site_C3_phase: Definition = {
+        "tensors": [
+            [
+                "tensor",
+                "tensor_conj",
+                "C1",
+                "T1",
+                "C2",
+                "T2",
+                "C3_phase",
+                "T3",
+                "C4",
+                "T4",
+            ]
+        ],
+        "network": [
+            [
+                (6, 7, -1, 10, 9),  # tensor
+                (13, 14, -2, 15, 16),  # tensor_conj
+                (2, 12),  # C1
+                (12, 9, 16, 3),  # T1
+                (3, 8),  # C2
+                (10, 15, 4, 8),  # T2
+                (11, 4),  # C3_phase
+                (1, 11, 14, 7),  # T3
+                (1, 5),  # C4
+                (5, 13, 6, 2),  # T4
+            ]
+        ],
+    }
+
+    density_matrix_one_site_C4_phase: Definition = {
+        "tensors": [
+            [
+                "tensor",
+                "tensor_conj",
+                "C1",
+                "T1",
+                "C2",
+                "T2",
+                "C3",
+                "T3",
+                "C4_phase",
+                "T4",
+            ]
+        ],
+        "network": [
+            [
+                (6, 7, -1, 10, 9),  # tensor
+                (13, 14, -2, 15, 16),  # tensor_conj
+                (2, 12),  # C1
+                (12, 9, 16, 3),  # T1
+                (3, 8),  # C2
+                (10, 15, 4, 8),  # T2
+                (11, 4),  # C3
+                (1, 11, 14, 7),  # T3
+                (1, 5),  # C4_phase
+                (5, 13, 6, 2),  # T4
+            ]
+        ],
+    }
+
+    density_matrix_one_site_T1_phase: Definition = {
+        "tensors": [
+            [
+                "tensor",
+                "tensor_conj",
+                "C1",
+                "T1_phase",
+                "C2",
+                "T2",
+                "C3",
+                "T3",
+                "C4",
+                "T4",
+            ]
+        ],
+        "network": [
+            [
+                (6, 7, -1, 10, 9),  # tensor
+                (13, 14, -2, 15, 16),  # tensor_conj
+                (2, 12),  # C1
+                (12, 9, 16, 3),  # T1_phase
+                (3, 8),  # C2
+                (10, 15, 4, 8),  # T2
+                (11, 4),  # C3
+                (1, 11, 14, 7),  # T3
+                (1, 5),  # C4
+                (5, 13, 6, 2),  # T4
+            ]
+        ],
+    }
+
+    density_matrix_one_site_T2_phase: Definition = {
+        "tensors": [
+            [
+                "tensor",
+                "tensor_conj",
+                "C1",
+                "T1",
+                "C2",
+                "T2_phase",
+                "C3",
+                "T3",
+                "C4",
+                "T4",
+            ]
+        ],
+        "network": [
+            [
+                (6, 7, -1, 10, 9),  # tensor
+                (13, 14, -2, 15, 16),  # tensor_conj
+                (2, 12),  # C1
+                (12, 9, 16, 3),  # T1
+                (3, 8),  # C2
+                (10, 15, 4, 8),  # T2_phase
+                (11, 4),  # C3
+                (1, 11, 14, 7),  # T3
+                (1, 5),  # C4
+                (5, 13, 6, 2),  # T4
+            ]
+        ],
+    }
+
+    density_matrix_one_site_T3_phase: Definition = {
+        "tensors": [
+            [
+                "tensor",
+                "tensor_conj",
+                "C1",
+                "T1",
+                "C2",
+                "T2",
+                "C3",
+                "T3_phase",
+                "C4",
+                "T4",
+            ]
+        ],
+        "network": [
+            [
+                (6, 7, -1, 10, 9),  # tensor
+                (13, 14, -2, 15, 16),  # tensor_conj
+                (2, 12),  # C1
+                (12, 9, 16, 3),  # T1
+                (3, 8),  # C2
+                (10, 15, 4, 8),  # T2
+                (11, 4),  # C3
+                (1, 11, 14, 7),  # T3_phase
+                (1, 5),  # C4
+                (5, 13, 6, 2),  # T4
+            ]
+        ],
+    }
+
+    density_matrix_one_site_T4_phase: Definition = {
+        "tensors": [
+            [
+                "tensor",
+                "tensor_conj",
+                "C1",
+                "T1",
+                "C2",
+                "T2",
+                "C3",
+                "T3",
+                "C4",
+                "T4_phase",
+            ]
+        ],
+        "network": [
+            [
+                (6, 7, -1, 10, 9),  # tensor
+                (13, 14, -2, 15, 16),  # tensor_conj
+                (2, 12),  # C1
+                (12, 9, 16, 3),  # T1
+                (3, 8),  # C2
+                (10, 15, 4, 8),  # T2
+                (11, 4),  # C3
+                (1, 11, 14, 7),  # T3
+                (1, 5),  # C4
+                (5, 13, 6, 2),  # T4_phase
+            ]
+        ],
+    }
+
     density_matrix_two_sites_left: Definition = {
         "tensors": [["tensor", "tensor_conj", "C1", "T1", "T3", "C4", "T4"]],
         "network": [
@@ -522,6 +770,51 @@ def _prepare_defs(cls):
     \\
     """
 
+    ctmrg_absorption_left_C1_phase_1: Definition = {
+        "tensors": [["C1_phase", "T1"], "projector_left_bottom"],
+        "network": [
+            [
+                (2, 1),  # C1_phase
+                (1, 3, 4, -2),  # T1
+            ],
+            (-1, 2, 3, 4),  # projector_left_bottom
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_L_C1.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C1 during left absorption with contraction order shown.
+
+       Contraction for C1 during left absorption. Here C1 is the tensor with
+       structure factor phase included which is grown by a normal T1 tensor.
+
+    \\
+    """
+
+    ctmrg_absorption_left_C1_phase_2: Definition = {
+        "tensors": [["C1", "T1_phase"], "projector_left_bottom"],
+        "network": [
+            [
+                (2, 1),  # C1
+                (1, 3, 4, -2),  # T1_phase
+            ],
+            (-1, 2, 3, 4),  # projector_left_bottom
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_L_C1.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C1 during left absorption with contraction order shown.
+
+       Contraction for C1 during left absorption. Here C1 is the tensor with
+       structure factor phase not included yet which is grown by a T1 tensor
+       which includes a phase already.
+
+    \\
+    """
+
     ctmrg_absorption_left_T4: Definition = {
         "tensors": [
             ["tensor", "tensor_conj", "T4"],
@@ -566,6 +859,42 @@ def _prepare_defs(cls):
         ],
     }
 
+    ctmrg_absorption_left_T4_large_d_phase_1: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T4_phase"],
+            "projector_left_top",
+            "projector_left_bottom",
+        ],
+        "network": [
+            [
+                (4, 8, 2, -3, 3),  # tensor
+                (5, 9, 2, -2, 6),  # tensor_conj
+                (7, 5, 4, 1),  # T4
+            ],
+            (1, 3, 6, -4),  # projector_left_top
+            (-1, 7, 8, 9),  # projector_left_bottom
+        ],
+    }
+
+    ctmrg_absorption_left_T4_large_d_phase_2: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T4"],
+            "projector_left_top",
+            "projector_left_bottom",
+            "structure_factor_gate",
+        ],
+        "network": [
+            [
+                (5, 9, 2, -3, 4),  # tensor
+                (6, 10, 3, -2, 7),  # tensor_conj
+                (8, 6, 5, 1),  # T4
+            ],
+            (1, 4, 7, -4),  # projector_left_top
+            (-1, 8, 9, 10),  # projector_left_bottom
+            (2, 3),  # structure_factor_gate
+        ],
+    }
+
     ctmrg_absorption_left_C4: Definition = {
         "tensors": [["T3", "C4"], "projector_left_top"],
         "network": [
@@ -587,70 +916,196 @@ def _prepare_defs(cls):
     \\
     """
 
-    ctmrg_absorption_right_C2: Definition = {
-        "tensors": [["T1", "C2"], "projector_right_bottom"],
+    ctmrg_absorption_left_C4_phase_1: Definition = {
+        "tensors": [["T3", "C4_phase"], "projector_left_top"],
         "network": [
             [
-                (-1, 3, 4, 1),  # T1
-                (1, 2),  # C2
+                (1, -1, 4, 3),  # T3
+                (1, 2),  # C4_phase
             ],
-            (2, 4, 3, -2),  # projector_right_bottom
+            (2, 3, 4, -2),  # projector_left_top
         ],
     }
     """
-    .. figure:: /images/CTMRG_Absorption_R_C2.*
+    .. figure:: /images/CTMRG_Absorption_L_C4.*
        :align: center
        :width: 60%
-       :alt: Contraction for C2 during right absorption with contraction order shown.
+       :alt: Contraction for C4 during left absorption with contraction order shown.
 
-       Contraction for C2 during right absorption.
+       Contraction for C4 during left absorption. Here C4 is the tensor with
+       structure factor phase included which is grown by a normal T3 tensor.
 
     \\
     """
 
-    ctmrg_absorption_right_T2: Definition = {
-        "tensors": [
-            ["tensor", "tensor_conj", "T2"],
-            "projector_right_top",
-            "projector_right_bottom",
-        ],
+    ctmrg_absorption_left_C4_phase_2: Definition = {
+        "tensors": [["T3_phase", "C4"], "projector_left_top"],
         "network": [
             [
-                (-1, 8, 6, 3, 2),  # tensor
-                (-2, 9, 6, 5, 4),  # tensor_conj
-                (3, 5, 7, 1),  # T2
+                (1, -1, 4, 3),  # T3_phase
+                (1, 2),  # C4
             ],
-            (-4, 1, 4, 2),  # projector_right_top
-            (7, 9, 8, -3),  # projector_right_bottom
+            (2, 3, 4, -2),  # projector_left_top
         ],
     }
     """
-    .. figure:: /images/CTMRG_Absorption_R_T2.*
+    .. figure:: /images/CTMRG_Absorption_L_C4.*
        :align: center
        :width: 60%
-       :alt: Contraction for T2 during right absorption with contraction order shown.
+       :alt: Contraction for C4 during left absorption with contraction order shown.
 
-       Contraction for T2 during right absorption.
+       Contraction for C4 during left absorption. Here C3 is the tensor with
+       structure factor phase not included yet which is grown by a T3 tensor
+       which includes a phase already.
 
     \\
     """
 
-    ctmrg_absorption_right_T2_large_d: Definition = {
-        "tensors": [
-            ["tensor", "tensor_conj", "T2"],
-            "projector_right_top",
-            "projector_right_bottom",
-        ],
+    ctmrg_absorption_right_C2: Definition = {
+        "tensors": [["T1", "C2"], "projector_right_bottom"],
         "network": [
             [
-                (-1, 8, 2, 4, 3),  # tensor
-                (-2, 9, 2, 6, 5),  # tensor_conj
-                (4, 6, 7, 1),  # T2
+                (-1, 3, 4, 1),  # T1
+                (1, 2),  # C2
             ],
-            (-4, 1, 5, 3),  # projector_right_top
+            (2, 4, 3, -2),  # projector_right_bottom
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_R_C2.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C2 during right absorption with contraction order shown.
+
+       Contraction for C2 during right absorption.
+
+    \\
+    """
+
+    ctmrg_absorption_right_C2_phase_1: Definition = {
+        "tensors": [["T1", "C2_phase"], "projector_right_bottom"],
+        "network": [
+            [
+                (-1, 3, 4, 1),  # T1
+                (1, 2),  # C2_phase
+            ],
+            (2, 4, 3, -2),  # projector_right_bottom
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_R_C2.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C2 during right absorption with contraction order shown.
+
+       Contraction for C2 during right absorption. Here C2 is the tensor with
+       structure factor phase included which is grown by a normal T1 tensor.
+
+    \\
+    """
+
+    ctmrg_absorption_right_C2_phase_2: Definition = {
+        "tensors": [["T1_phase", "C2"], "projector_right_bottom"],
+        "network": [
+            [
+                (-1, 3, 4, 1),  # T1_phase
+                (1, 2),  # C2
+            ],
+            (2, 4, 3, -2),  # projector_right_bottom
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_R_C2.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C2 during right absorption with contraction order shown.
+
+       Contraction for C2 during right absorption. Here C2 is the tensor with
+       structure factor phase not included yet which is grown by a T1 tensor
+       which includes a phase already.
+
+    \\
+    """
+
+    ctmrg_absorption_right_T2: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T2"],
+            "projector_right_top",
+            "projector_right_bottom",
+        ],
+        "network": [
+            [
+                (-1, 8, 6, 3, 2),  # tensor
+                (-2, 9, 6, 5, 4),  # tensor_conj
+                (3, 5, 7, 1),  # T2
+            ],
+            (-4, 1, 4, 2),  # projector_right_top
             (7, 9, 8, -3),  # projector_right_bottom
         ],
     }
+    """
+    .. figure:: /images/CTMRG_Absorption_R_T2.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for T2 during right absorption with contraction order shown.
+
+       Contraction for T2 during right absorption.
+
+    \\
+    """
+
+    ctmrg_absorption_right_T2_large_d: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T2"],
+            "projector_right_top",
+            "projector_right_bottom",
+        ],
+        "network": [
+            [
+                (-1, 8, 2, 4, 3),  # tensor
+                (-2, 9, 2, 6, 5),  # tensor_conj
+                (4, 6, 7, 1),  # T2
+            ],
+            (-4, 1, 5, 3),  # projector_right_top
+            (7, 9, 8, -3),  # projector_right_bottom
+        ],
+    }
+
+    ctmrg_absorption_right_T2_large_d_phase_1: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T2_phase"],
+            "projector_right_top",
+            "projector_right_bottom",
+        ],
+        "network": [
+            [
+                (-1, 8, 2, 4, 3),  # tensor
+                (-2, 9, 2, 6, 5),  # tensor_conj
+                (4, 6, 7, 1),  # T2_phase
+            ],
+            (-4, 1, 5, 3),  # projector_right_top
+            (7, 9, 8, -3),  # projector_right_bottom
+        ],
+    }
+
+    ctmrg_absorption_right_T2_large_d_phase_2: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T2"],
+            "projector_right_top",
+            "projector_right_bottom",
+            "structure_factor_gate",
+        ],
+        "network": [
+            [
+                (-1, 9, 2, 5, 4),  # tensor
+                (-2, 10, 3, 7, 6),  # tensor_conj
+                (5, 7, 8, 1),  # T2_phase
+            ],
+            (-4, 1, 6, 4),  # projector_right_top
+            (8, 10, 9, -3),  # projector_right_bottom
+            (2, 3),  # structure_factor_gate
+        ],
+    }
 
     ctmrg_absorption_right_C3: Definition = {
         "tensors": [["C3", "T3"], "projector_right_top"],
@@ -673,6 +1128,51 @@ def _prepare_defs(cls):
     \\
     """
 
+    ctmrg_absorption_right_C3_phase_1: Definition = {
+        "tensors": [["C3_phase", "T3"], "projector_right_top"],
+        "network": [
+            [
+                (1, 2),  # C3_phase
+                (-1, 1, 4, 3),  # T3
+            ],
+            (-2, 2, 4, 3),  # projector_right_top
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_R_C3.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C3 during right absorption with contraction order shown.
+
+       Contraction for C3 during right absorption. Here C3 is the tensor with
+       structure factor phase included which is grown by a normal T3 tensor.
+
+    \\
+    """
+
+    ctmrg_absorption_right_C3_phase_2: Definition = {
+        "tensors": [["C3", "T3_phase"], "projector_right_top"],
+        "network": [
+            [
+                (1, 2),  # C3
+                (-1, 1, 4, 3),  # T3_phase
+            ],
+            (-2, 2, 4, 3),  # projector_right_top
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_R_C3.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C3 during right absorption with contraction order shown.
+
+       Contraction for C3 during right absorption. Here C3 is the tensor with
+       structure factor phase not included yet which is grown by a T3 tensor
+       which includes a phase already.
+
+    \\
+    """
+
     ctmrg_absorption_top_C1: Definition = {
         "tensors": [["T4", "C1"], "projector_top_right"],
         "network": [
@@ -694,6 +1194,51 @@ def _prepare_defs(cls):
     \\
     """
 
+    ctmrg_absorption_top_C1_phase_1: Definition = {
+        "tensors": [["T4", "C1_phase"], "projector_top_right"],
+        "network": [
+            [
+                (-1, 4, 3, 1),  # T4
+                (1, 2),  # C1_phase
+            ],
+            (2, 3, 4, -2),  # projector_top_right
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_U_C1.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C1 during top absorption with contraction order shown.
+
+       Contraction for C1 during top absorption. Here C1 is the tensor with
+       structure factor phase included which is grown by a normal T4 tensor.
+
+    \\
+    """
+
+    ctmrg_absorption_top_C1_phase_2: Definition = {
+        "tensors": [["T4_phase", "C1"], "projector_top_right"],
+        "network": [
+            [
+                (-1, 4, 3, 1),  # T4_phase
+                (1, 2),  # C1
+            ],
+            (2, 3, 4, -2),  # projector_top_right
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_U_C1.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C1 during top absorption with contraction order shown.
+
+       Contraction for C1 during top absorption. Here C1 is the tensor with
+       structure factor phase not included yet which is grown by a T4 tensor
+       which includes a phase already.
+
+    \\
+    """
+
     ctmrg_absorption_top_T1: Definition = {
         "tensors": [
             ["tensor", "tensor_conj", "T1"],
@@ -738,6 +1283,42 @@ def _prepare_defs(cls):
         ],
     }
 
+    ctmrg_absorption_top_T1_large_d_phase_1: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T1_phase"],
+            "projector_top_left",
+            "projector_top_right",
+        ],
+        "network": [
+            [
+                (4, -2, 2, 8, 3),  # tensor
+                (6, -3, 2, 9, 5),  # tensor_conj
+                (1, 3, 5, 7),  # T1_phase
+            ],
+            (-1, 1, 4, 6),  # projector_top_left
+            (7, 8, 9, -4),  # projector_top_right
+        ],
+    }
+
+    ctmrg_absorption_top_T1_large_d_phase_2: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T1"],
+            "projector_top_left",
+            "projector_top_right",
+            "structure_factor_gate",
+        ],
+        "network": [
+            [
+                (5, -2, 2, 9, 4),  # tensor
+                (7, -3, 3, 10, 6),  # tensor_conj
+                (1, 4, 6, 8),  # T1
+            ],
+            (-1, 1, 5, 7),  # projector_top_left
+            (8, 9, 10, -4),  # projector_top_right
+            (2, 3),  # structure_factor_gate
+        ],
+    }
+
     ctmrg_absorption_top_C2: Definition = {
         "tensors": [["C2", "T2"], "projector_top_left"],
         "network": [
@@ -759,6 +1340,51 @@ def _prepare_defs(cls):
     \\
     """
 
+    ctmrg_absorption_top_C2_phase_1: Definition = {
+        "tensors": [["C2_phase", "T2"], "projector_top_left"],
+        "network": [
+            [
+                (2, 1),  # C2_phase
+                (3, 4, -2, 1),  # T2
+            ],
+            (-1, 2, 3, 4),  # projector_top_left
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_U_C2.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C2 during top absorption with contraction order shown.
+
+       Contraction for C2 during top absorption. Here C2 is the tensor with
+       structure factor phase included which is grown by a normal T2 tensor.
+
+    \\
+    """
+
+    ctmrg_absorption_top_C2_phase_2: Definition = {
+        "tensors": [["C2", "T2_phase"], "projector_top_left"],
+        "network": [
+            [
+                (2, 1),  # C2
+                (3, 4, -2, 1),  # T2_phase
+            ],
+            (-1, 2, 3, 4),  # projector_top_left
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_U_C2.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C2 during top absorption with contraction order shown.
+
+       Contraction for C2 during top absorption. Here C2 is the tensor with
+       structure factor phase not included yet which is grown by a T2 tensor
+       which includes a phase already.
+
+    \\
+    """
+
     ctmrg_absorption_bottom_C4: Definition = {
         "tensors": [["C4", "T4"], "projector_bottom_right"],
         "network": [
@@ -780,6 +1406,51 @@ def _prepare_defs(cls):
     \\
     """
 
+    ctmrg_absorption_bottom_C4_phase_1: Definition = {
+        "tensors": [["C4_phase", "T4"], "projector_bottom_right"],
+        "network": [
+            [
+                (2, 1),  # C4_phase
+                (1, 4, 3, -2),  # T4
+            ],
+            (-1, 2, 4, 3),  # projector_bottom_right
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_D_C4.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C4 during bottom absorption with contraction order shown.
+
+       Contraction for C4 during bottom absorption. Here C4 is the tensor with
+       structure factor phase included which is grown by a normal T4 tensor.
+
+    \\
+    """
+
+    ctmrg_absorption_bottom_C4_phase_2: Definition = {
+        "tensors": [["C4", "T4_phase"], "projector_bottom_right"],
+        "network": [
+            [
+                (2, 1),  # C4
+                (1, 4, 3, -2),  # T4_phase
+            ],
+            (-1, 2, 4, 3),  # projector_bottom_right
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_D_C4.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C4 during bottom absorption with contraction order shown.
+
+       Contraction for C4 during bottom absorption. Here C4 is the tensor with
+       structure factor phase not included yet which is grown by a T4 tensor
+       which includes a phase already.
+
+    \\
+    """
+
     ctmrg_absorption_bottom_T3: Definition = {
         "tensors": [
             ["tensor", "tensor_conj", "T3"],
@@ -824,6 +1495,42 @@ def _prepare_defs(cls):
         ],
     }
 
+    ctmrg_absorption_bottom_T3_large_d_phase_1: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T3_phase"],
+            "projector_bottom_left",
+            "projector_bottom_right",
+        ],
+        "network": [
+            [
+                (4, 3, 2, 8, -4),  # tensor
+                (6, 5, 2, 9, -3),  # tensor_conj
+                (1, 7, 5, 3),  # T3_phase
+            ],
+            (1, 6, 4, -1),  # projector_bottom_left
+            (-2, 7, 9, 8),  # projector_bottom_right
+        ],
+    }
+
+    ctmrg_absorption_bottom_T3_large_d_phase_2: Definition = {
+        "tensors": [
+            ["tensor", "tensor_conj", "T3"],
+            "projector_bottom_left",
+            "projector_bottom_right",
+            "structure_factor_gate",
+        ],
+        "network": [
+            [
+                (5, 4, 2, 9, -4),  # tensor
+                (7, 6, 3, 10, -3),  # tensor_conj
+                (1, 8, 6, 4),  # T3
+            ],
+            (1, 7, 5, -1),  # projector_bottom_left
+            (-2, 8, 10, 9),  # projector_bottom_right
+            (2, 3),  # structure_factor_gate
+        ],
+    }
+
     ctmrg_absorption_bottom_C3: Definition = {
         "tensors": [["T2", "C3"], "projector_bottom_left"],
         "network": [
@@ -845,6 +1552,51 @@ def _prepare_defs(cls):
     \\
     """
 
+    ctmrg_absorption_bottom_C3_phase_1: Definition = {
+        "tensors": [["T2", "C3_phase"], "projector_bottom_left"],
+        "network": [
+            [
+                (3, 4, 1, -2),  # T2
+                (2, 1),  # C3_phase
+            ],
+            (2, 4, 3, -1),  # projector_bottom_left
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_D_C3.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C3 during bottom absorption with contraction order shown.
+
+       Contraction for C3 during bottom absorption. Here C3 is the tensor with
+       structure factor phase included which is grown by a normal T2 tensor.
+
+    \\
+    """
+
+    ctmrg_absorption_bottom_C3_phase_2: Definition = {
+        "tensors": [["T2_phase", "C3"], "projector_bottom_left"],
+        "network": [
+            [
+                (3, 4, 1, -2),  # T2_phase
+                (2, 1),  # C3
+            ],
+            (2, 4, 3, -1),  # projector_bottom_left
+        ],
+    }
+    """
+    .. figure:: /images/CTMRG_Absorption_D_C3.*
+       :align: center
+       :width: 60%
+       :alt: Contraction for C3 during bottom absorption with contraction order shown.
+
+       Contraction for C3 during bottom absorption. Here C3 is the tensor with
+       structure factor phase not included yet which is grown by a T2 tensor
+       which includes a phase already.
+
+    \\
+    """
+
     ctmrg_gauge_fix_T1: Definition = {
         "tensors": [["T1"], "left_unitary", "right_unitary"],
         "network": [
diff --git a/varipeps/ctmrg/__init__.py b/varipeps/ctmrg/__init__.py
index a4eb14c..93f562f 100644
--- a/varipeps/ctmrg/__init__.py
+++ b/varipeps/ctmrg/__init__.py
@@ -1,6 +1,8 @@
 from . import absorption
 from . import projectors
 from . import routine
+from . import structure_factor_absorption
+from . import structure_factor_routine
 
 from .routine import (
     calc_ctmrg_env,
@@ -8,3 +10,5 @@
     CTMRGNotConvergedError,
     CTMRGGradientNotConvergedError,
 )
+
+from .structure_factor_routine import calc_ctmrg_env_structure_factor
diff --git a/varipeps/ctmrg/structure_factor_absorption.py b/varipeps/ctmrg/structure_factor_absorption.py
new file mode 100644
index 0000000..5a9a526
--- /dev/null
+++ b/varipeps/ctmrg/structure_factor_absorption.py
@@ -0,0 +1,909 @@
+import collections.abc
+from dataclasses import dataclass, field
+from operator import itemgetter
+
+import jax.numpy as jnp
+from jax import jit
+from jax.lax import scan, cond
+
+from varipeps.peps import PEPS_Tensor, PEPS_Unit_Cell
+from varipeps.contractions import apply_contraction, apply_contraction_jitted
+from varipeps.utils.svd import gauge_fixed_svd
+from varipeps.utils.periodic_indices import calculate_periodic_indices
+from varipeps.utils.projector_dict import Projector_Dict
+from .projectors import (
+    calc_left_projectors,
+    calc_right_projectors,
+    calc_top_projectors,
+    calc_bottom_projectors,
+)
+from varipeps.expectation.one_site import calc_one_site_single_gate_obj
+from varipeps.config import VariPEPS_Config
+from varipeps.global_state import VariPEPS_Global_State
+
+
+from typing import Sequence, Tuple, List, Dict, Literal
+
+CTMRG_Orientation = Literal["top-left", "top-right", "bottom-left", "bottom-right"]
+
+
+def _tensor_list_from_indices(
+    peps_tensors: Sequence[jnp.ndarray], indices: Sequence[Sequence[int]]
+) -> List[List[jnp.ndarray]]:
+    return [[peps_tensors[ty] for ty in tx] for tx in indices]
+
+
+def _get_ctmrg_2x2_structure(
+    peps_tensors: Sequence[jnp.ndarray],
+    view: PEPS_Unit_Cell,
+    orientation: CTMRG_Orientation,
+) -> Tuple[List[List[jnp.ndarray]], List[List[PEPS_Tensor]]]:
+    if orientation == "top-left":
+        x_slice = slice(0, 2, None)
+        y_slice = slice(0, 2, None)
+    elif orientation == "top-right":
+        x_slice = slice(0, 2, None)
+        y_slice = slice(-1, 1, None)
+    elif orientation == "bottom-left":
+        x_slice = slice(-1, 1, None)
+        y_slice = slice(0, 2, None)
+    elif orientation == "bottom-right":
+        x_slice = slice(-1, 1, None)
+        y_slice = slice(-1, 1, None)
+    else:
+        raise ValueError("Invalid orientation.")
+
+    indices = view.get_indices((x_slice, y_slice))
+    view_tensors = _tensor_list_from_indices(peps_tensors, indices)
+
+    view_tensor_objs = view[x_slice, y_slice]
+
+    return view_tensors, view_tensor_objs
+
+
+def do_left_absorption_structure_factor(
+    peps_tensors: Sequence[jnp.ndarray],
+    unitcell: PEPS_Unit_Cell,
+    structure_factor_gates: Sequence[jnp.ndarray],
+    structure_factor_outer_factor: float,
+    structure_factor_inner_factors: Sequence[float],
+    config: VariPEPS_Config,
+    state: VariPEPS_Global_State,
+) -> PEPS_Unit_Cell:
+    """
+    Calculate the left CTMRG tensors after one absorption step and returns
+    the updated unitcell. This routine also calculates the tensors including
+    the phase factor for a structure factor calculation.
+
+    Args:
+      peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence of unique PEPS tensors the unitcell consists of.
+      unitcell (:obj:`~varipeps.peps.PEPS_Unit_Cell`):
+        The unitcell to work on.
+      structure_factor_gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence with the observables which is absorbed into the CTM tensors
+        containing the phase for the structure factor calculation. Expected to
+        be a sequence where the gate is already multiplied with identities to
+        match the physical dimension of the coarse-grained tensor
+      structure_factor_outer_factor (:obj:`float`):
+        The factor used to calculate the new tensors by shifting one site in
+        the square lattice to the left. Likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      structure_factor_inner_factors (:term:`sequence` of :obj:`float`):
+        For coarse-grained systems the sequence with the factors used to
+        calculate the phase by shifting one site inside one coarse-grained
+        square site. Set it to None, [] or [1] if system has
+        no coarsed-grained structure. If used likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      config (:obj:`~varipeps.config.VariPEPS_Config`):
+        Global configuration object of the variPEPS library. Please see its
+        class definition for details.
+      state (:obj:`~varipeps.global_state.VariPEPS_Global_State`):
+        Global state object of the variPEPS library. It is used to transport
+        a common state across different parts of the framework. Please see its
+        class definition for details.
+    Returns:
+      :obj:`~varipeps.peps.PEPS_Unit_Cell`:
+        New instance of the unitcell with the updated left CTMRG tensors of
+        all elements of the unitcell.
+    """
+    max_x, max_y = unitcell.get_size()
+    left_projectors = Projector_Dict(max_x=max_x, max_y=max_y)
+
+    working_unitcell = unitcell.copy()
+
+    smallest_S_list = []
+
+    if (
+        structure_factor_inner_factors is None
+        or len(structure_factor_inner_factors) == 0
+    ):
+        structure_factor_inner_factors = (1,)
+
+    for y, iter_columns in working_unitcell.iter_all_columns(only_unique=True):
+        column_views = [view for view in iter_columns]
+
+        for x, view in column_views:
+            left_proj, smallest_S = calc_left_projectors(
+                *_get_ctmrg_2x2_structure(peps_tensors, view, "top-left"), config, state
+            )
+            left_projectors[(x, y)] = left_proj
+            smallest_S_list.append(smallest_S)
+
+        new_C1 = []
+        new_T4 = []
+        new_C4 = []
+        new_C1_phase = []
+        new_T4_phase = []
+        new_C4_phase = []
+
+        for x, view in column_views:
+            working_tensor = peps_tensors[view.get_indices((0, 0))[0][0]]
+            working_tensor_obj = view[0, 0][0][0]
+
+            C1_projector = left_projectors.get_projector(x, y, -1, 0).bottom
+            new_C1_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_left_C1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C1_projector],
+            )
+            new_C1_phase_tmp_1 = apply_contraction_jitted(
+                "ctmrg_absorption_left_C1_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C1_projector],
+            )
+            new_C1_phase_tmp_2 = apply_contraction_jitted(
+                "ctmrg_absorption_left_C1_phase_2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C1_projector],
+            )
+            new_C1_phase_tmp = (
+                new_C1_phase_tmp_1 + new_C1_phase_tmp_2
+            ) * structure_factor_outer_factor
+            new_C1_tmp_norm = jnp.linalg.norm(new_C1_tmp)
+            new_C1.append(new_C1_tmp / new_C1_tmp_norm)
+            new_C1_phase.append(new_C1_phase_tmp / new_C1_tmp_norm / 2)
+
+            T4_projector_top = left_projectors.get_projector(x, y, -1, 0).top
+            T4_projector_bottom = left_projectors.get_projector(x, y, 0, 0).bottom
+            new_T4_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_left_T4_large_d",
+                [working_tensor],
+                [working_tensor_obj],
+                [T4_projector_top, T4_projector_bottom],
+            )
+            new_T4_phase_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_left_T4_large_d_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [T4_projector_top, T4_projector_bottom],
+            )
+
+            for i, factor in enumerate(structure_factor_inner_factors):
+                new_T4_phase_tmp += (
+                    apply_contraction_jitted(
+                        "ctmrg_absorption_left_T4_large_d_phase_2",
+                        [working_tensor],
+                        [working_tensor_obj],
+                        [
+                            T4_projector_top,
+                            T4_projector_bottom,
+                            structure_factor_gates[i],
+                        ],
+                    )
+                    * factor
+                )
+
+            new_T4_phase_tmp = new_T4_phase_tmp * structure_factor_outer_factor
+            new_T4_tmp_norm = jnp.linalg.norm(new_T4_tmp)
+            new_T4.append(new_T4_tmp / new_T4_tmp_norm)
+            new_T4_phase.append(
+                new_T4_phase_tmp
+                / new_T4_tmp_norm
+                / (1 + len(structure_factor_inner_factors))
+            )
+
+            C4_projector = left_projectors.get_projector(x, y, 0, 0).top
+            new_C4_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_left_C4",
+                [working_tensor],
+                [working_tensor_obj],
+                [C4_projector],
+            )
+            new_C4_phase_tmp_1 = apply_contraction_jitted(
+                "ctmrg_absorption_left_C4_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C4_projector],
+            )
+            new_C4_phase_tmp_2 = apply_contraction_jitted(
+                "ctmrg_absorption_left_C4_phase_2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C4_projector],
+            )
+            new_C4_phase_tmp = (
+                new_C4_phase_tmp_1 + new_C4_phase_tmp_2
+            ) * structure_factor_outer_factor
+            new_C4_tmp_norm = jnp.linalg.norm(new_C4_tmp)
+            new_C4.append(new_C4_tmp / new_C4_tmp_norm)
+            new_C4_phase.append(new_C4_phase_tmp / new_C4_tmp_norm / 2)
+
+        for x, view in column_views:
+            view[0, 1] = view[0, 1][0][0].replace_left_env_tensors(
+                new_C1[x],
+                new_T4[x],
+                new_C4[x],
+                new_C1_phase[x],
+                new_T4_phase[x],
+                new_C4_phase[x],
+            )
+
+    return working_unitcell, smallest_S_list
+
+
+def do_right_absorption_structure_factor(
+    peps_tensors: Sequence[jnp.ndarray],
+    unitcell: PEPS_Unit_Cell,
+    structure_factor_gates: Sequence[jnp.ndarray],
+    structure_factor_outer_factor: float,
+    structure_factor_inner_factors: Sequence[float],
+    config: VariPEPS_Config,
+    state: VariPEPS_Global_State,
+) -> PEPS_Unit_Cell:
+    """
+    Calculate the right CTMRG tensors after one absorption step and returns
+    the updated unitcell. This routine also calculates the tensors including
+    the phase factor for a structure factor calculation.
+
+    Args:
+      peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence of unique PEPS tensors the unitcell consists of.
+      unitcell (:obj:`~varipeps.peps.PEPS_Unit_Cell`):
+        The unitcell to work on.
+      structure_factor_gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence with the observables which is absorbed into the CTM tensors
+        containing the phase for the structure factor calculation. Expected to
+        be a sequence where the gate is already multiplied with identities to
+        match the physical dimension of the coarse-grained tensor
+      structure_factor_outer_factor (:obj:`float`):
+        The factor used to calculate the new tensors by shifting one site in
+        the square lattice to the right. Likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      structure_factor_inner_factors (:term:`sequence` of :obj:`float`):
+        For coarse-grained systems the sequence with the factors used to
+        calculate the phase by shifting one site inside one coarse-grained
+        square site. Set it to None, [] or [1] if system has
+        no coarsed-grained structure. If used likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      config (:obj:`~varipeps.config.VariPEPS_Config`):
+        Global configuration object of the variPEPS library. Please see its
+        class definition for details.
+      state (:obj:`~varipeps.global_state.VariPEPS_Global_State`):
+        Global state object of the variPEPS library. It is used to transport
+        a common state across different parts of the framework. Please see its
+        class definition for details.
+    Returns:
+      :obj:`~varipeps.peps.PEPS_Unit_Cell`:
+        New instance of the unitcell with the updated right CTMRG tensors of
+        all elements of the unitcell.
+    """
+    max_x, max_y = unitcell.get_size()
+    right_projectors = Projector_Dict(max_x=max_x, max_y=max_y)
+
+    working_unitcell = unitcell.copy()
+
+    smallest_S_list = []
+
+    if (
+        structure_factor_inner_factors is None
+        or len(structure_factor_inner_factors) == 0
+    ):
+        structure_factor_inner_factors = (1,)
+
+    for y, iter_columns in working_unitcell.iter_all_columns(
+        reverse=True, only_unique=True
+    ):
+        column_views = [view for view in iter_columns]
+
+        for x, view in column_views:
+            right_proj, smallest_S = calc_right_projectors(
+                *_get_ctmrg_2x2_structure(peps_tensors, view, "top-right"),
+                config,
+                state
+            )
+            right_projectors[(x, y)] = right_proj
+            smallest_S_list.append(smallest_S)
+
+        new_C2 = []
+        new_T2 = []
+        new_C3 = []
+        new_C2_phase = []
+        new_T2_phase = []
+        new_C3_phase = []
+
+        for x, view in column_views:
+            working_tensor = peps_tensors[view.get_indices((0, 0))[0][0]]
+            working_tensor_obj = view[0, 0][0][0]
+
+            C2_projector = right_projectors.get_projector(x, y, -1, 0).bottom
+            new_C2_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_right_C2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C2_projector],
+            )
+            new_C2_phase_tmp_1 = apply_contraction_jitted(
+                "ctmrg_absorption_right_C2_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C2_projector],
+            )
+            new_C2_phase_tmp_2 = apply_contraction_jitted(
+                "ctmrg_absorption_right_C2_phase_2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C2_projector],
+            )
+            new_C2_phase_tmp = (
+                new_C2_phase_tmp_1 + new_C2_phase_tmp_2
+            ) * structure_factor_outer_factor
+            new_C2_tmp_norm = jnp.linalg.norm(new_C2_tmp)
+            new_C2.append(new_C2_tmp / new_C2_tmp_norm)
+            new_C2_phase.append(new_C2_phase_tmp / new_C2_tmp_norm / 2)
+
+            T2_projector_top = right_projectors.get_projector(x, y, -1, 0).top
+            T2_projector_bottom = right_projectors.get_projector(x, y, 0, 0).bottom
+            new_T2_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_right_T2_large_d",
+                [working_tensor],
+                [working_tensor_obj],
+                [T2_projector_top, T2_projector_bottom],
+            )
+            new_T2_phase_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_right_T2_large_d_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [T2_projector_top, T2_projector_bottom],
+            )
+
+            for i, factor in enumerate(structure_factor_inner_factors):
+                new_T2_phase_tmp += (
+                    apply_contraction_jitted(
+                        "ctmrg_absorption_right_T2_large_d_phase_2",
+                        [working_tensor],
+                        [working_tensor_obj],
+                        [
+                            T2_projector_top,
+                            T2_projector_bottom,
+                            structure_factor_gates[i],
+                        ],
+                    )
+                    * factor
+                )
+
+            new_T2_phase_tmp = new_T2_phase_tmp * structure_factor_outer_factor
+            new_T2_tmp_norm = jnp.linalg.norm(new_T2_tmp)
+            new_T2.append(new_T2_tmp / new_T2_tmp_norm)
+            new_T2_phase.append(
+                new_T2_phase_tmp
+                / new_T2_tmp_norm
+                / (1 + len(structure_factor_inner_factors))
+            )
+
+            C3_projector = right_projectors.get_projector(x, y, 0, 0).top
+            new_C3_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_right_C3",
+                [working_tensor],
+                [working_tensor_obj],
+                [C3_projector],
+            )
+            new_C3_phase_tmp_1 = apply_contraction_jitted(
+                "ctmrg_absorption_right_C3_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C3_projector],
+            )
+            new_C3_phase_tmp_2 = apply_contraction_jitted(
+                "ctmrg_absorption_right_C3_phase_2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C3_projector],
+            )
+            new_C3_phase_tmp = (
+                new_C3_phase_tmp_1 + new_C3_phase_tmp_2
+            ) * structure_factor_outer_factor
+            new_C3_tmp_norm = jnp.linalg.norm(new_C3_tmp)
+            new_C3.append(new_C3_tmp / new_C3_tmp_norm)
+            new_C3_phase.append(new_C3_phase_tmp / new_C3_tmp_norm / 2)
+
+        for x, view in column_views:
+            view[0, -1] = view[0, -1][0][0].replace_right_env_tensors(
+                new_C2[x],
+                new_T2[x],
+                new_C3[x],
+                new_C2_phase[x],
+                new_T2_phase[x],
+                new_C3_phase[x],
+            )
+
+    return working_unitcell, smallest_S_list
+
+
+def do_top_absorption_structure_factor(
+    peps_tensors: Sequence[jnp.ndarray],
+    unitcell: PEPS_Unit_Cell,
+    structure_factor_gates: Sequence[jnp.ndarray],
+    structure_factor_outer_factor: float,
+    structure_factor_inner_factors: Sequence[float],
+    config: VariPEPS_Config,
+    state: VariPEPS_Global_State,
+) -> PEPS_Unit_Cell:
+    """
+    Calculate the top CTMRG tensors after one absorption step and returns
+    the updated unitcell. This routine also calculates the tensors including
+    the phase factor for a structure factor calculation.
+
+    Args:
+      peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence of unique PEPS tensors the unitcell consists of.
+      unitcell (:obj:`~varipeps.peps.PEPS_Unit_Cell`):
+        The unitcell to work on.
+      structure_factor_gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence with the observables which is absorbed into the CTM tensors
+        containing the phase for the structure factor calculation. Expected to
+        be a sequence where the gate is already multiplied with identities to
+        match the physical dimension of the coarse-grained tensor
+      structure_factor_outer_factor (:obj:`float`):
+        The factor used to calculate the new tensors by shifting one site in
+        the square lattice to the top. Likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      structure_factor_inner_factors (:term:`sequence` of :obj:`float`):
+        For coarse-grained systems the sequence with the factors used to
+        calculate the phase by shifting one site inside one coarse-grained
+        square site. Set it to None, [] or [1] if system has
+        no coarsed-grained structure. If used likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      config (:obj:`~varipeps.config.VariPEPS_Config`):
+        Global configuration object of the variPEPS library. Please see its
+        class definition for details.
+      state (:obj:`~varipeps.global_state.VariPEPS_Global_State`):
+        Global state object of the variPEPS library. It is used to transport
+        a common state across different parts of the framework. Please see its
+        class definition for details.
+    Returns:
+      :obj:`~varipeps.peps.PEPS_Unit_Cell`:
+        New instance of the unitcell with the updated top CTMRG tensors of
+        all elements of the unitcell.
+    """
+    max_x, max_y = unitcell.get_size()
+    top_projectors = Projector_Dict(max_x=max_x, max_y=max_y)
+
+    working_unitcell = unitcell.copy()
+
+    smallest_S_list = []
+
+    if (
+        structure_factor_inner_factors is None
+        or len(structure_factor_inner_factors) == 0
+    ):
+        structure_factor_inner_factors = (1,)
+
+    for x, iter_rows in working_unitcell.iter_all_rows(only_unique=True):
+        row_views = [view for view in iter_rows]
+
+        for y, view in row_views:
+            top_proj, smallest_S = calc_top_projectors(
+                *_get_ctmrg_2x2_structure(peps_tensors, view, "top-left"), config, state
+            )
+            top_projectors[(x, y)] = top_proj
+            smallest_S_list.append(smallest_S)
+
+        new_C1 = []
+        new_T1 = []
+        new_C2 = []
+        new_C1_phase = []
+        new_T1_phase = []
+        new_C2_phase = []
+
+        for y, view in row_views:
+            working_tensor = peps_tensors[view.get_indices((0, 0))[0][0]]
+            working_tensor_obj = view[0, 0][0][0]
+
+            C1_projector = top_projectors.get_projector(x, y, 0, -1).right  # type: ignore
+            new_C1_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_top_C1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C1_projector],
+            )
+            new_C1_phase_tmp_1 = apply_contraction_jitted(
+                "ctmrg_absorption_top_C1_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C1_projector],
+            )
+            new_C1_phase_tmp_2 = apply_contraction_jitted(
+                "ctmrg_absorption_top_C1_phase_2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C1_projector],
+            )
+            new_C1_phase_tmp = (
+                new_C1_phase_tmp_1 + new_C1_phase_tmp_2
+            ) * structure_factor_outer_factor
+            new_C1_tmp_norm = jnp.linalg.norm(new_C1_tmp)
+            new_C1.append(new_C1_tmp / new_C1_tmp_norm)
+            new_C1_phase.append(new_C1_phase_tmp / new_C1_tmp_norm / 2)
+
+            T1_projector_left = top_projectors.get_projector(x, y, 0, -1).left  # type: ignore
+            T1_projector_right = top_projectors.get_projector(x, y, 0, 0).right  # type: ignore
+            new_T1_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_top_T1_large_d",
+                [working_tensor],
+                [working_tensor_obj],
+                [T1_projector_left, T1_projector_right],
+            )
+            new_T1_phase_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_top_T1_large_d_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [T1_projector_left, T1_projector_right],
+            )
+
+            for i, factor in enumerate(structure_factor_inner_factors):
+                new_T1_phase_tmp += (
+                    apply_contraction_jitted(
+                        "ctmrg_absorption_top_T1_large_d_phase_2",
+                        [working_tensor],
+                        [working_tensor_obj],
+                        [
+                            T1_projector_left,
+                            T1_projector_right,
+                            structure_factor_gates[i],
+                        ],
+                    )
+                    * factor
+                )
+
+            new_T1_phase_tmp = new_T1_phase_tmp * structure_factor_outer_factor
+            new_T1_tmp_norm = jnp.linalg.norm(new_T1_tmp)
+            new_T1.append(new_T1_tmp / new_T1_tmp_norm)
+            new_T1_phase.append(
+                new_T1_phase_tmp
+                / new_T1_tmp_norm
+                / (1 + len(structure_factor_inner_factors))
+            )
+
+            C2_projector = top_projectors.get_projector(x, y, 0, 0).left  # type: ignore
+            new_C2_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_top_C2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C2_projector],
+            )
+            new_C2_phase_tmp_1 = apply_contraction_jitted(
+                "ctmrg_absorption_top_C2_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C2_projector],
+            )
+            new_C2_phase_tmp_2 = apply_contraction_jitted(
+                "ctmrg_absorption_top_C2_phase_2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C2_projector],
+            )
+            new_C2_phase_tmp = (
+                new_C2_phase_tmp_1 + new_C2_phase_tmp_2
+            ) * structure_factor_outer_factor
+            new_C2_tmp_norm = jnp.linalg.norm(new_C2_tmp)
+            new_C2.append(new_C2_tmp / new_C2_tmp_norm)
+            new_C2_phase.append(new_C2_phase_tmp / new_C2_tmp_norm / 2)
+
+        for y, view in row_views:
+            view[1, 0] = view[1, 0][0][0].replace_top_env_tensors(
+                new_C1[y],
+                new_T1[y],
+                new_C2[y],
+                new_C1_phase[y],
+                new_T1_phase[y],
+                new_C2_phase[y],
+            )
+
+    return working_unitcell, smallest_S_list
+
+
+def do_bottom_absorption_structure_factor(
+    peps_tensors: Sequence[jnp.ndarray],
+    unitcell: PEPS_Unit_Cell,
+    structure_factor_gates: Sequence[jnp.ndarray],
+    structure_factor_outer_factor: float,
+    structure_factor_inner_factors: Sequence[float],
+    config: VariPEPS_Config,
+    state: VariPEPS_Global_State,
+) -> PEPS_Unit_Cell:
+    """
+    Calculate the bottom CTMRG tensors after one absorption step and returns
+    the updated unitcell. This routine also calculates the tensors including
+    the phase factor for a structure factor calculation.
+
+    Args:
+      peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence of unique PEPS tensors the unitcell consists of.
+      unitcell (:obj:`~varipeps.peps.PEPS_Unit_Cell`):
+        The unitcell to work on.
+      structure_factor_gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence with the observables which is absorbed into the CTM tensors
+        containing the phase for the structure factor calculation. Expected to
+        be a sequence where the gate is already multiplied with identities to
+        match the physical dimension of the coarse-grained tensor
+      structure_factor_outer_factor (:obj:`float`):
+        The factor used to calculate the new tensors by shifting one site in
+        the square lattice to the bottom. Likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      structure_factor_inner_factors (:term:`sequence` of :obj:`float`):
+        For coarse-grained systems the sequence with the factors used to
+        calculate the phase by shifting one site inside one coarse-grained
+        square site. Set it to None, [] or [1] if system has
+        no coarsed-grained structure. If used likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      config (:obj:`~varipeps.config.VariPEPS_Config`):
+        Global configuration object of the variPEPS library. Please see its
+        class definition for details.
+      state (:obj:`~varipeps.global_state.VariPEPS_Global_State`):
+        Global state object of the variPEPS library. It is used to transport
+        a common state across different parts of the framework. Please see its
+        class definition for details.
+    Returns:
+      :obj:`~varipeps.peps.PEPS_Unit_Cell`:
+        New instance of the unitcell with the updated bottom CTMRG tensors of
+        all elements of the unitcell.
+    """
+    max_x, max_y = unitcell.get_size()
+    bottom_projectors = Projector_Dict(max_x=max_x, max_y=max_y)
+
+    working_unitcell = unitcell.copy()
+
+    smallest_S_list = []
+
+    if (
+        structure_factor_inner_factors is None
+        or len(structure_factor_inner_factors) == 0
+    ):
+        structure_factor_inner_factors = (1,)
+
+    for x, iter_rows in working_unitcell.iter_all_rows(reverse=True, only_unique=True):
+        row_views = [view for view in iter_rows]
+
+        for y, view in row_views:
+            bottom_proj, smallest_S = calc_bottom_projectors(
+                *_get_ctmrg_2x2_structure(peps_tensors, view, "bottom-left"),
+                config,
+                state
+            )
+            bottom_projectors[(x, y)] = bottom_proj
+            smallest_S_list.append(smallest_S)
+
+        new_C4 = []
+        new_T3 = []
+        new_C3 = []
+        new_C4_phase = []
+        new_T3_phase = []
+        new_C3_phase = []
+
+        for y, view in row_views:
+            working_tensor = peps_tensors[view.get_indices((0, 0))[0][0]]
+            working_tensor_obj = view[0, 0][0][0]
+
+            C4_projector = bottom_projectors.get_projector(x, y, 0, -1).right  # type: ignore
+            new_C4_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_bottom_C4",
+                [working_tensor],
+                [working_tensor_obj],
+                [C4_projector],
+            )
+            new_C4_phase_tmp_1 = apply_contraction_jitted(
+                "ctmrg_absorption_bottom_C4_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C4_projector],
+            )
+            new_C4_phase_tmp_2 = apply_contraction_jitted(
+                "ctmrg_absorption_bottom_C4_phase_2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C4_projector],
+            )
+            new_C4_phase_tmp = (
+                new_C4_phase_tmp_1 + new_C4_phase_tmp_2
+            ) * structure_factor_outer_factor
+            new_C4_tmp_norm = jnp.linalg.norm(new_C4_tmp)
+            new_C4.append(new_C4_tmp / new_C4_tmp_norm)
+            new_C4_phase.append(new_C4_phase_tmp / new_C4_tmp_norm / 2)
+
+            T3_projector_left = bottom_projectors.get_projector(x, y, 0, -1).left  # type: ignore
+            T3_projector_right = bottom_projectors.get_projector(x, y, 0, 0).right  # type: ignore
+            new_T3_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_bottom_T3_large_d",
+                [working_tensor],
+                [working_tensor_obj],
+                [T3_projector_left, T3_projector_right],
+            )
+            new_T3_phase_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_bottom_T3_large_d_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [T3_projector_left, T3_projector_right],
+            )
+
+            for i, factor in enumerate(structure_factor_inner_factors):
+                new_T3_phase_tmp += (
+                    apply_contraction_jitted(
+                        "ctmrg_absorption_bottom_T3_large_d_phase_2",
+                        [working_tensor],
+                        [working_tensor_obj],
+                        [
+                            T3_projector_left,
+                            T3_projector_right,
+                            structure_factor_gates[i],
+                        ],
+                    )
+                    * factor
+                )
+
+            new_T3_phase_tmp = new_T3_phase_tmp * structure_factor_outer_factor
+            new_T3_tmp_norm = jnp.linalg.norm(new_T3_tmp)
+            new_T3.append(new_T3_tmp / new_T3_tmp_norm)
+            new_T3_phase.append(
+                new_T3_phase_tmp
+                / new_T3_tmp_norm
+                / (1 + len(structure_factor_inner_factors))
+            )
+
+            C3_projector = bottom_projectors.get_projector(x, y, 0, 0).left  # type: ignore
+            new_C3_tmp = apply_contraction_jitted(
+                "ctmrg_absorption_bottom_C3",
+                [working_tensor],
+                [working_tensor_obj],
+                [C3_projector],
+            )
+            new_C3_phase_tmp_1 = apply_contraction_jitted(
+                "ctmrg_absorption_bottom_C3_phase_1",
+                [working_tensor],
+                [working_tensor_obj],
+                [C3_projector],
+            )
+            new_C3_phase_tmp_2 = apply_contraction_jitted(
+                "ctmrg_absorption_bottom_C3_phase_2",
+                [working_tensor],
+                [working_tensor_obj],
+                [C3_projector],
+            )
+            new_C3_phase_tmp = (
+                new_C3_phase_tmp_1 + new_C3_phase_tmp_2
+            ) * structure_factor_outer_factor
+            new_C3_tmp_norm = jnp.linalg.norm(new_C3_tmp)
+            new_C3.append(new_C3_tmp / new_C3_tmp_norm)
+            new_C3_phase.append(new_C3_phase_tmp / new_C3_tmp_norm / 2)
+
+        for y, view in row_views:
+            view[-1, 0] = view[-1, 0][0][0].replace_bottom_env_tensors(
+                new_C4[y],
+                new_T3[y],
+                new_C3[y],
+                new_C4_phase[y],
+                new_T3_phase[y],
+                new_C3_phase[y],
+            )
+
+    return working_unitcell, smallest_S_list
+
+
+def do_absorption_step_structure_factor(
+    peps_tensors: Sequence[jnp.ndarray],
+    unitcell: PEPS_Unit_Cell,
+    structure_factor_gates: Sequence[jnp.ndarray],
+    structure_factor_outer_factors: Sequence[float],
+    structure_factor_inner_factors: Sequence[float],
+    config: VariPEPS_Config,
+    state: VariPEPS_Global_State,
+) -> PEPS_Unit_Cell:
+    """
+    Calculate the all CTMRG tensors after one absorption step and returns
+    the updated unitcell. This routine also calculates the tensors including
+    the phase factor for a structure factor calculation.
+
+    Args:
+      peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence of unique PEPS tensors the unitcell consists of.
+      unitcell (:obj:`~varipeps.peps.PEPS_Unit_Cell`):
+        The unitcell to work on.
+      structure_factor_gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence with the observables which is absorbed into the CTM tensors
+        containing the phase for the structure factor calculation. Expected to
+        be a sequence where the gate is already multiplied with identities to
+        match the physical dimension of the coarse-grained tensor
+      structure_factor_outer_factors (:obj:`float`):
+        The sequence with factors used to calculate the new tensors by shifting
+        one site in the square lattice. Likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``. If length two, the first
+        argument will be used for bottom absorption and its complex conjugate for
+        top and the second one for right and its complex conjugate for left
+        absorption. If length four, it will be used in the order
+        (top, bottom, left, right).
+      structure_factor_inner_factors (:term:`sequence` of :obj:`float`):
+        For coarse-grained systems the sequence with the factors used to
+        calculate the phase by shifting one site inside one coarse-grained
+        square site. Set it to None, [] or [1] if system has
+        no coarsed-grained structure. If used likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+      config (:obj:`~varipeps.config.VariPEPS_Config`):
+        Global configuration object of the variPEPS library. Please see its
+        class definition for details.
+      state (:obj:`~varipeps.global_state.VariPEPS_Global_State`):
+        Global state object of the variPEPS library. It is used to transport
+        a common state across different parts of the framework. Please see its
+        class definition for details.
+    Returns:
+      :obj:`~varipeps.peps.PEPS_Unit_Cell`:
+        New instance of the unitcell with the all updated CTMRG tensors of
+        all elements of the unitcell.
+    """
+
+    if len(structure_factor_outer_factors) == 2:
+        structure_factor_outer_factors = (
+            structure_factor_outer_factors[0].conj(),
+            structure_factor_outer_factors[0],
+            structure_factor_outer_factors[1].conj(),
+            structure_factor_outer_factors[1],
+        )
+    if len(structure_factor_outer_factors) != 4:
+        raise ValueError("Length mismatch for outer factor list.")
+
+    result, left_smallest_S = do_left_absorption_structure_factor(
+        peps_tensors,
+        unitcell,
+        structure_factor_gates,
+        structure_factor_outer_factors[2],
+        structure_factor_inner_factors,
+        config,
+        state,
+    )
+    result, top_smallest_S = do_top_absorption_structure_factor(
+        peps_tensors,
+        result,
+        structure_factor_gates,
+        structure_factor_outer_factors[0],
+        structure_factor_inner_factors,
+        config,
+        state,
+    )
+    result, right_smallest_S = do_right_absorption_structure_factor(
+        peps_tensors,
+        result,
+        structure_factor_gates,
+        structure_factor_outer_factors[3],
+        structure_factor_inner_factors,
+        config,
+        state,
+    )
+    result, bottom_smallest_S = do_bottom_absorption_structure_factor(
+        peps_tensors,
+        result,
+        structure_factor_gates,
+        structure_factor_outer_factors[1],
+        structure_factor_inner_factors,
+        config,
+        state,
+    )
+    norm_smallest_S = jnp.linalg.norm(
+        jnp.asarray(
+            left_smallest_S + top_smallest_S + right_smallest_S + bottom_smallest_S
+        ),
+        ord=jnp.inf,
+    )
+    return result, norm_smallest_S
diff --git a/varipeps/ctmrg/structure_factor_routine.py b/varipeps/ctmrg/structure_factor_routine.py
new file mode 100644
index 0000000..ddb5d96
--- /dev/null
+++ b/varipeps/ctmrg/structure_factor_routine.py
@@ -0,0 +1,407 @@
+from functools import partial
+import enum
+
+import jax.numpy as jnp
+from jax import jit, custom_vjp, vjp, tree_util
+import jax.util
+from jax.lax import cond, while_loop
+import jax.debug as jdebug
+
+from varipeps import varipeps_config, varipeps_global_state
+from varipeps.peps import PEPS_Tensor, PEPS_Unit_Cell
+from varipeps.utils.debug_print import debug_print
+from .structure_factor_absorption import do_absorption_step_structure_factor
+from .routine import CTMRGNotConvergedError
+
+from typing import Sequence, Tuple, List, Optional
+
+
+@enum.unique
+class CTM_Enum_Structure_Factor(enum.IntEnum):
+    C1 = enum.auto()
+    C2 = enum.auto()
+    C3 = enum.auto()
+    C4 = enum.auto()
+    C1_Phase = enum.auto()
+    C2_Phase = enum.auto()
+    C3_Phase = enum.auto()
+    C4_Phase = enum.auto()
+    T1 = enum.auto()
+    T2 = enum.auto()
+    T3 = enum.auto()
+    T4 = enum.auto()
+
+
+@partial(jit, static_argnums=(2,), inline=True)
+def _calc_corner_svds_structure_factor(
+    peps_tensors: List[PEPS_Tensor],
+    old_corner_svd: jnp.ndarray,
+    tensor_shape: Optional[Tuple[int, int, int]],
+) -> jnp.ndarray:
+    if tensor_shape is None:
+        step_corner_svd = jnp.zeros_like(old_corner_svd)
+    else:
+        step_corner_svd = jnp.zeros(tensor_shape, dtype=jnp.float64)
+
+    for ti, t in enumerate(peps_tensors):
+        C1_svd = jnp.linalg.svd(t.C1, full_matrices=False, compute_uv=False)
+        step_corner_svd = step_corner_svd.at[ti, 0, : C1_svd.shape[0]].set(
+            C1_svd, indices_are_sorted=True, unique_indices=True
+        )
+
+        C2_svd = jnp.linalg.svd(t.C2, full_matrices=False, compute_uv=False)
+        step_corner_svd = step_corner_svd.at[ti, 1, : C2_svd.shape[0]].set(
+            C2_svd, indices_are_sorted=True, unique_indices=True
+        )
+
+        C3_svd = jnp.linalg.svd(t.C3, full_matrices=False, compute_uv=False)
+        step_corner_svd = step_corner_svd.at[ti, 2, : C3_svd.shape[0]].set(
+            C3_svd, indices_are_sorted=True, unique_indices=True
+        )
+
+        C4_svd = jnp.linalg.svd(t.C4, full_matrices=False, compute_uv=False)
+        step_corner_svd = step_corner_svd.at[ti, 3, : C4_svd.shape[0]].set(
+            C4_svd, indices_are_sorted=True, unique_indices=True
+        )
+
+        C1_phase_svd = jnp.linalg.svd(t.C1_phase, full_matrices=False, compute_uv=False)
+        step_corner_svd = step_corner_svd.at[ti, 4, : C1_phase_svd.shape[0]].set(
+            C1_phase_svd, indices_are_sorted=True, unique_indices=True
+        )
+
+        C2_phase_svd = jnp.linalg.svd(t.C2_phase, full_matrices=False, compute_uv=False)
+        step_corner_svd = step_corner_svd.at[ti, 5, : C2_phase_svd.shape[0]].set(
+            C2_phase_svd, indices_are_sorted=True, unique_indices=True
+        )
+
+        C3_phase_svd = jnp.linalg.svd(t.C3_phase, full_matrices=False, compute_uv=False)
+        step_corner_svd = step_corner_svd.at[ti, 6, : C3_phase_svd.shape[0]].set(
+            C3_phase_svd, indices_are_sorted=True, unique_indices=True
+        )
+
+        C4_phase_svd = jnp.linalg.svd(t.C4_phase, full_matrices=False, compute_uv=False)
+        step_corner_svd = step_corner_svd.at[ti, 7, : C4_phase_svd.shape[0]].set(
+            C4_phase_svd, indices_are_sorted=True, unique_indices=True
+        )
+
+    return step_corner_svd
+
+
+@jit
+def _ctmrg_body_func_structure_factor(carry):
+    (
+        w_tensors,
+        w_unitcell_last_step,
+        converged,
+        last_corner_svd,
+        eps,
+        count,
+        norm_smallest_S,
+        structure_factor_gates,
+        structure_factor_outer_factors,
+        structure_factor_inner_factors,
+        state,
+        config,
+    ) = carry
+
+    w_unitcell, norm_smallest_S = do_absorption_step_structure_factor(
+        w_tensors,
+        w_unitcell_last_step,
+        structure_factor_gates,
+        structure_factor_outer_factors,
+        structure_factor_inner_factors,
+        config,
+        state,
+    )
+
+    verbose_data = [] if config.ctmrg_verbose_output else None
+    if last_corner_svd is None:
+        corner_svd = None
+        converged = False
+        measure = jnp.nan
+    else:
+        corner_svd = _calc_corner_svds_structure_factor(
+            w_unitcell.get_unique_tensors(), last_corner_svd, None
+        )
+        measure = jnp.linalg.norm(corner_svd - last_corner_svd)
+        converged = measure < eps
+
+    if config.ctmrg_print_steps:
+        debug_print("CTMRG: {}: {}", count, measure)
+        if config.ctmrg_verbose_output:
+            for ti, ctm_enum_i, diff in verbose_data:
+                debug_print(
+                    "CTMRG: Verbose: ti {}, CTM tensor {}, Diff {}",
+                    ti,
+                    CTM_Enum(ctm_enum_i).name,
+                    diff,
+                )
+
+    count += 1
+
+    return (
+        w_tensors,
+        w_unitcell,
+        converged,
+        corner_svd,
+        eps,
+        count,
+        norm_smallest_S,
+        structure_factor_gates,
+        structure_factor_outer_factors,
+        structure_factor_inner_factors,
+        state,
+        config,
+    )
+
+
+@jit
+def _ctmrg_while_wrapper_structure_factor(start_carry):
+    def cond_func(carry):
+        _, _, converged, _, _, count, _, _, _, _, _, config = carry
+        return jnp.logical_not(converged) & (count < config.ctmrg_max_steps)
+
+    (
+        _,
+        working_unitcell,
+        converged,
+        _,
+        _,
+        end_count,
+        norm_smallest_S,
+        _,
+        _,
+        _,
+        _,
+        _,
+    ) = while_loop(cond_func, _ctmrg_body_func_structure_factor, start_carry)
+
+    return working_unitcell, converged, end_count, norm_smallest_S
+
+
+def calc_ctmrg_env_structure_factor(
+    peps_tensors: Sequence[jnp.ndarray],
+    unitcell: PEPS_Unit_Cell,
+    structure_factor_gates: Sequence[jnp.ndarray],
+    structure_factor_outer_factors: Sequence[float],
+    structure_factor_inner_factors: Sequence[float],
+    *,
+    eps: Optional[float] = None,
+    _return_truncation_eps: bool = False,
+) -> PEPS_Unit_Cell:
+    """
+    Calculate the new converged CTMRG tensors for the unit cell. The function
+    updates the environment all iPEPS tensors in the unit cell according to the
+    periodic structure. This routine also calculates the tensors including
+    the phase factor for a structure factor calculation.
+
+    Args:
+      peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence of unique PEPS tensors the unitcell consists of.
+      unitcell (:obj:`~varipeps.peps.PEPS_Unit_Cell`):
+        The unitcell to work on.
+      structure_factor_gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
+        The sequence with the observables which is absorbed into the CTM tensors
+        containing the phase for the structure factor calculation. Expected to
+        be a sequence where the gate is already multiplied with identities to
+        match the physical dimension of the coarse-grained tensor
+      structure_factor_outer_factors (:obj:`float`):
+        The sequence with factors used to calculate the new tensors by shifting
+        one site in the square lattice. Likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``. If length two, the first
+        argument will be used for bottom absorption and its complex conjugate for
+        top and the second one for right and its complex conjugate for left
+        absorption. If length four, it will be used in the order
+        (top, bottom, left, right).
+      structure_factor_inner_factors (:term:`sequence` of :obj:`float`):
+        For coarse-grained systems the sequence with the factors used to
+        calculate the phase by shifting one site inside one coarse-grained
+        square site. Set it to None, [] or [1] if system has
+        no coarsed-grained structure. If used likely something like
+        ``jnp.exp(- 1j * q_vector @ r_vector)``.
+    Keyword args:
+      eps (:obj:`float`):
+        The convergence criterion.
+    Returns:
+      :obj:`~varipeps.peps.PEPS_Unit_Cell`:
+        New instance of the unitcell with all updated converged CTMRG tensors of
+        all elements of the unitcell.
+    """
+    eps = eps if eps is not None else varipeps_config.ctmrg_convergence_eps
+
+    shape_corner_svd = (
+        unitcell.get_len_unique_tensors(),
+        8,
+        unitcell[0, 0][0][0].chi,
+    )
+    init_corner_singular_vals = _calc_corner_svds_structure_factor(
+        unitcell.get_unique_tensors(), None, shape_corner_svd
+    )
+
+    initial_unitcell = unitcell
+    working_unitcell = unitcell
+    varipeps_global_state.ctmrg_effective_truncation_eps = None
+
+    norm_smallest_S = jnp.nan
+    already_tried_chi = {working_unitcell[0, 0][0][0].chi}
+
+    while True:
+        tmp_count = 0
+        corner_singular_vals = None
+
+        while any(
+            i.C1.shape[0] != i.chi for i in working_unitcell.get_unique_tensors()
+        ):
+            (
+                _,
+                working_unitcell,
+                _,
+                corner_singular_vals,
+                _,
+                tmp_count,
+                _,
+                _,
+                _,
+                _,
+                _,
+                _,
+            ) = _ctmrg_body_func_structure_factor(
+                (
+                    peps_tensors,
+                    working_unitcell,
+                    False,
+                    init_corner_singular_vals,
+                    eps,
+                    tmp_count,
+                    jnp.inf,
+                    structure_factor_gates,
+                    structure_factor_outer_factors,
+                    structure_factor_inner_factors,
+                    varipeps_global_state,
+                    varipeps_config,
+                )
+            )
+
+        working_unitcell, converged, end_count, norm_smallest_S = (
+            _ctmrg_while_wrapper_structure_factor(
+                (
+                    peps_tensors,
+                    working_unitcell,
+                    False,
+                    (
+                        corner_singular_vals
+                        if corner_singular_vals is not None
+                        else init_corner_singular_vals
+                    ),
+                    eps,
+                    tmp_count,
+                    jnp.inf,
+                    structure_factor_gates,
+                    structure_factor_outer_factors,
+                    structure_factor_inner_factors,
+                    varipeps_global_state,
+                    varipeps_config,
+                )
+            )
+        )
+
+        current_truncation_eps = (
+            varipeps_config.ctmrg_truncation_eps
+            if varipeps_global_state.ctmrg_effective_truncation_eps is None
+            else varipeps_global_state.ctmrg_effective_truncation_eps
+        )
+
+        if (
+            varipeps_config.ctmrg_heuristic_increase_chi
+            and norm_smallest_S > varipeps_config.ctmrg_heuristic_increase_chi_threshold
+            and working_unitcell[0, 0][0][0].chi < working_unitcell[0, 0][0][0].max_chi
+        ):
+            new_chi = (
+                working_unitcell[0, 0][0][0].chi
+                + varipeps_config.ctmrg_heuristic_increase_chi_step_size
+            )
+            if new_chi > working_unitcell[0, 0][0][0].max_chi:
+                new_chi = working_unitcell[0, 0][0][0].max_chi
+
+            if not new_chi in already_tried_chi:
+                working_unitcell = working_unitcell.change_chi(new_chi)
+                initial_unitcell = initial_unitcell.change_chi(new_chi)
+
+                if varipeps_config.ctmrg_print_steps:
+                    debug_print(
+                        "CTMRG: Increasing chi to {} since smallest SVD Norm was {}.",
+                        new_chi,
+                        norm_smallest_S,
+                    )
+
+                already_tried_chi.add(new_chi)
+
+                continue
+        elif (
+            varipeps_config.ctmrg_heuristic_decrease_chi
+            and norm_smallest_S < current_truncation_eps
+            and working_unitcell[0, 0][0][0].chi > 2
+        ):
+            new_chi = (
+                working_unitcell[0, 0][0][0].chi
+                - varipeps_config.ctmrg_heuristic_decrease_chi_step_size
+            )
+            if new_chi < 2:
+                new_chi = 2
+
+            if not new_chi in already_tried_chi:
+                working_unitcell = working_unitcell.change_chi(new_chi)
+
+                if varipeps_config.ctmrg_print_steps:
+                    debug_print(
+                        "CTMRG: Decreasing chi to {} since smallest SVD Norm was {}.",
+                        new_chi,
+                        norm_smallest_S,
+                    )
+
+                already_tried_chi.add(new_chi)
+
+                continue
+
+        if (
+            varipeps_config.ctmrg_increase_truncation_eps
+            and end_count == varipeps_config.ctmrg_max_steps
+            and not converged
+        ):
+            new_truncation_eps = (
+                current_truncation_eps
+                * varipeps_config.ctmrg_increase_truncation_eps_factor
+            )
+            if (
+                new_truncation_eps
+                <= varipeps_config.ctmrg_increase_truncation_eps_max_value
+            ):
+                if varipeps_config.ctmrg_print_steps:
+                    debug_print(
+                        "CTMRG: Increasing SVD truncation eps to {}.",
+                        new_truncation_eps,
+                    )
+                varipeps_global_state.ctmrg_effective_truncation_eps = (
+                    new_truncation_eps
+                )
+                working_unitcell = initial_unitcell
+                already_tried_chi = {working_unitcell[0, 0][0][0].chi}
+                continue
+
+        break
+
+    if _return_truncation_eps:
+        last_truncation_eps = varipeps_global_state.ctmrg_effective_truncation_eps
+    varipeps_global_state.ctmrg_effective_truncation_eps = None
+
+    if (
+        varipeps_config.ctmrg_fail_if_not_converged
+        and end_count == varipeps_config.ctmrg_max_steps
+        and not converged
+    ):
+        raise CTMRGNotConvergedError
+
+    if _return_truncation_eps:
+        return working_unitcell, last_truncation_eps, norm_smallest_S
+
+    return working_unitcell, norm_smallest_S
diff --git a/varipeps/expectation/__init__.py b/varipeps/expectation/__init__.py
index 2fb20c9..8c3a142 100644
--- a/varipeps/expectation/__init__.py
+++ b/varipeps/expectation/__init__.py
@@ -1,4 +1,5 @@
 from . import spiral_helpers
+from . import structure_factor
 from . import model
 from . import one_site
 from . import two_sites
diff --git a/varipeps/expectation/structure_factor.py b/varipeps/expectation/structure_factor.py
new file mode 100644
index 0000000..4ab3c52
--- /dev/null
+++ b/varipeps/expectation/structure_factor.py
@@ -0,0 +1,177 @@
+from functools import partial
+
+import jax.numpy as jnp
+from jax import jit
+
+from varipeps.peps import PEPS_Tensor, PEPS_Unit_Cell
+from varipeps.contractions import apply_contraction_jitted
+
+from typing import Sequence
+
+
+@partial(jit, static_argnums=(4, 5))
+def calc_structure_factor_expectation(
+    peps_tensor_obj: PEPS_Tensor,
+    alpha_gate: jnp.ndarray,
+    beta_gate: jnp.array,
+    structure_factor_inner_factors: Sequence[float],
+    real_d: int,
+    num_sites: int,
+):
+    if num_sites > 1:
+        Id = jnp.eye(real_d ** (num_sites - 1))
+
+        full_alpha_gate = [jnp.kron(alpha_gate, Id)]
+
+        alpha_gate_tmp = full_alpha_gate[0].reshape((real_d,) * 2 * num_sites)
+        for i in range(1, num_sites):
+            trans_order = list(range(1, num_sites)) + list(
+                range(num_sites + 1, 2 * num_sites)
+            )
+            trans_order.insert(i, 0)
+            trans_order.insert(num_sites + i, num_sites)
+
+            tmp_gate = alpha_gate_tmp.transpose(trans_order).reshape(
+                real_d**num_sites, real_d**num_sites
+            )
+
+            full_alpha_gate.append(tmp_gate * structure_factor_inner_factors[i].conj())
+
+        alpha_beta_gate = 0
+        # alpha_beta_gate_tmp_1 = alpha_beta_gate.reshape((real_d,) * 2 * num_sites)
+        alpha_beta_gate_tmp_2 = jnp.kron(
+            jnp.kron(alpha_gate, beta_gate), jnp.eye(real_d ** (num_sites - 2))
+        ).reshape((real_d,) * 2 * num_sites)
+
+        for i in range(num_sites):
+            for j in range(num_sites):
+                if i == j:
+                    continue
+
+                # if i == j:
+                #     trans_order = list(range(1, num_sites)) + list(
+                #         range(num_sites + 1, 2 * num_sites)
+                #     )
+                #     trans_order.insert(i, 0)
+                #     trans_order.insert(num_sites + i, num_sites)
+                #
+                #     tmp_gate = alpha_beta_gate_tmp_1.transpose(trans_order)
+                #     tmp_gate = tmp_gate.reshape(real_d**num_sites, real_d**num_sites)
+                #
+                #     alpha_beta_gate += tmp_gate
+                # else:
+                trans_order = list(range(2, num_sites)) + list(
+                    range(num_sites + 2, 2 * num_sites)
+                )
+                if i <= j:
+                    trans_order.insert(i, 0)
+                    trans_order.insert(j, 1)
+                    trans_order.insert(num_sites + i, num_sites)
+                    trans_order.insert(num_sites + j, num_sites + 1)
+                else:
+                    trans_order.insert(j, 1)
+                    trans_order.insert(i, 0)
+                    trans_order.insert(num_sites + j, num_sites + 1)
+                    trans_order.insert(num_sites + i, num_sites)
+
+                tmp_gate = alpha_beta_gate_tmp_2.transpose(trans_order)
+                tmp_gate = tmp_gate.reshape(real_d**num_sites, real_d**num_sites)
+
+                alpha_beta_gate += (
+                    tmp_gate
+                    * structure_factor_inner_factors[i].conj()
+                    * structure_factor_inner_factors[j]
+                )
+    else:
+        full_alpha_gate = [alpha_gate]
+        alpha_beta_gate = alpha_gate @ beta_gate
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site", [peps_tensor_obj.tensor], [peps_tensor_obj], []
+    )
+
+    norm = jnp.trace(density_matrix)
+
+    result = jnp.tensordot(density_matrix, alpha_beta_gate, ((0, 1), (0, 1))) / norm
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site_C1_phase",
+        [peps_tensor_obj.tensor],
+        [peps_tensor_obj],
+        [],
+    )
+
+    for g in full_alpha_gate:
+        result += jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site_C2_phase",
+        [peps_tensor_obj.tensor],
+        [peps_tensor_obj],
+        [],
+    )
+
+    for g in full_alpha_gate:
+        result += jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site_C3_phase",
+        [peps_tensor_obj.tensor],
+        [peps_tensor_obj],
+        [],
+    )
+
+    for g in full_alpha_gate:
+        result += jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site_C4_phase",
+        [peps_tensor_obj.tensor],
+        [peps_tensor_obj],
+        [],
+    )
+
+    for g in full_alpha_gate:
+        result += jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site_T1_phase",
+        [peps_tensor_obj.tensor],
+        [peps_tensor_obj],
+        [],
+    )
+
+    for g in full_alpha_gate:
+        result += jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site_T2_phase",
+        [peps_tensor_obj.tensor],
+        [peps_tensor_obj],
+        [],
+    )
+
+    for g in full_alpha_gate:
+        result += jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site_T3_phase",
+        [peps_tensor_obj.tensor],
+        [peps_tensor_obj],
+        [],
+    )
+
+    for g in full_alpha_gate:
+        result += jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm
+
+    density_matrix = apply_contraction_jitted(
+        "density_matrix_one_site_T4_phase",
+        [peps_tensor_obj.tensor],
+        [peps_tensor_obj],
+        [],
+    )
+
+    for g in full_alpha_gate:
+        result += jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm
+
+    return result
diff --git a/varipeps/optimization/optimizer.py b/varipeps/optimization/optimizer.py
index 16937d4..7926617 100644
--- a/varipeps/optimization/optimizer.py
+++ b/varipeps/optimization/optimizer.py
@@ -186,7 +186,7 @@ def autosave_function(
     filename: PathLike,
     tensors: jnp.ndarray,
     unitcell: PEPS_Unit_Cell,
-    counter: Optional[int] = None,
+    counter: Optional[Union[int, str]] = None,
     auxiliary_data: Optional[Dict[str, Any]] = None,
 ) -> None:
     if counter is not None:
@@ -197,6 +197,52 @@ def autosave_function(
         unitcell.save_to_file(filename, auxiliary_data=auxiliary_data)
 
 
+def _autosave_wrapper(
+    autosave_func,
+    autosave_filename,
+    working_tensors,
+    working_unitcell,
+    working_value,
+    counter,
+    best_run,
+    max_trunc_error_list,
+    step_energies,
+    step_chi,
+    step_conv,
+    spiral_indices,
+    additional_input,
+):
+    auxiliary_data = {
+        "best_run": best_run if best_run is not None else 0,
+        "current_energy": working_value,
+    }
+
+    for k in sorted(max_trunc_error_list.keys()):
+        auxiliary_data[f"max_trunc_error_list_{k:d}"] = max_trunc_error_list[k]
+        auxiliary_data[f"step_energies_{k:d}"] = step_energies[k]
+        auxiliary_data[f"step_chi_{k:d}"] = step_chi[k]
+        auxiliary_data[f"step_conv_{k:d}"] = step_conv[k]
+
+    if spiral_indices is not None:
+        for spiral_i in spiral_indices:
+            auxiliary_data[f"spiral_vector_{spiral_i:d}"] = working_tensors[spiral_i]
+    elif additional_input.get("spiral_vectors") is not None:
+        add_input_spiral = additional_input.get("spiral_vectors")
+        if isinstance(add_input_spiral, jnp.ndarray):
+            add_input_spiral = (add_input_spiral,)
+        for spiral_i, elem in enumerate(add_input_spiral):
+            spiral_i += 1
+            auxiliary_data[f"spiral_vector_{spiral_i:d}"] = elem
+
+    autosave_func(
+        autosave_filename,
+        working_tensors,
+        working_unitcell,
+        counter=counter,
+        auxiliary_data=auxiliary_data,
+    )
+
+
 def optimize_peps_network(
     input_tensors: Union[PEPS_Unit_Cell, Sequence[jnp.ndarray]],
     expectation_func: Expectation_Model,
@@ -256,6 +302,10 @@ def random_noise(a):
         if isinstance(input_tensors, collections.abc.Sequence) and isinstance(
             input_tensors[0], PEPS_Unit_Cell
         ):
+            if len(input_tensors[0].get_unique_tensors()) != 1:
+                raise ValueError(
+                    "You want to use spiral PEPS but you use a unit cell with more than one site. Seems wrong to me!"
+                )
             working_tensors = cast(
                 List[jnp.ndarray],
                 [i.tensor for i in input_tensors[0].get_unique_tensors()],
@@ -467,6 +517,22 @@ def random_noise(a):
                             best_unitcell = working_unitcell
                             best_run = random_noise_retries
 
+                            _autosave_wrapper(
+                                autosave_func,
+                                autosave_filename,
+                                working_tensors,
+                                working_unitcell,
+                                working_value,
+                                "best",
+                                best_run,
+                                max_trunc_error_list,
+                                step_energies,
+                                step_chi,
+                                step_conv,
+                                spiral_indices,
+                                additional_input,
+                            )
+
                         if isinstance(input_tensors, PEPS_Unit_Cell) or (
                             isinstance(input_tensors, collections.abc.Sequence)
                             and isinstance(input_tensors[0], PEPS_Unit_Cell)
@@ -577,37 +643,20 @@ def random_noise(a):
             pbar.refresh()
 
             if count % varipeps_config.optimizer_autosave_step_count == 0:
-                auxiliary_data = {
-                    "best_run": best_run if best_run is not None else 0,
-                }
-
-                for k in sorted(max_trunc_error_list.keys()):
-                    auxiliary_data[f"max_trunc_error_list_{k:d}"] = (
-                        max_trunc_error_list[k]
-                    )
-                    auxiliary_data[f"step_energies_{k:d}"] = step_energies[k]
-                    auxiliary_data[f"step_chi_{k:d}"] = step_chi[k]
-                    auxiliary_data[f"step_conv_{k:d}"] = step_conv[k]
-
-                if spiral_indices is not None:
-                    for spiral_i in spiral_indices:
-                        auxiliary_data[f"spiral_vector_{spiral_i:d}"] = working_tensors[
-                            spiral_i
-                        ]
-                elif additional_input.get("spiral_vectors") is not None:
-                    add_input_spiral = additional_input.get("spiral_vectors")
-                    if isinstance(add_input_spiral, jnp.ndarray):
-                        add_input_spiral = (add_input_spiral,)
-                    for spiral_i, elem in enumerate(add_input_spiral):
-                        spiral_i += 1
-                        auxiliary_data[f"spiral_vector_{spiral_i:d}"] = elem
-
-                autosave_func(
+                _autosave_wrapper(
+                    autosave_func,
                     autosave_filename,
                     working_tensors,
                     working_unitcell,
-                    counter=random_noise_retries,
-                    auxiliary_data=auxiliary_data,
+                    working_value,
+                    random_noise_retries,
+                    best_run,
+                    max_trunc_error_list,
+                    step_energies,
+                    step_chi,
+                    step_conv,
+                    spiral_indices,
+                    additional_input,
                 )
 
     if working_value < best_value:
@@ -616,6 +665,22 @@ def random_noise(a):
         best_unitcell = working_unitcell
         best_run = random_noise_retries
 
+        _autosave_wrapper(
+            autosave_func,
+            autosave_filename,
+            working_tensors,
+            working_unitcell,
+            working_value,
+            "best",
+            best_run,
+            max_trunc_error_list,
+            step_energies,
+            step_chi,
+            step_conv,
+            spiral_indices,
+            additional_input,
+        )
+
     print(f"Best energy result found: {best_value}")
 
     return OptimizeResult(
diff --git a/varipeps/peps/__init__.py b/varipeps/peps/__init__.py
index c6f08d9..4ab0d7c 100644
--- a/varipeps/peps/__init__.py
+++ b/varipeps/peps/__init__.py
@@ -1,4 +1,4 @@
 from . import tensor
 from . import unitcell
-from .tensor import PEPS_Tensor
+from .tensor import PEPS_Tensor, PEPS_Tensor_Structure_Factor
 from .unitcell import PEPS_Unit_Cell
diff --git a/varipeps/peps/tensor.py b/varipeps/peps/tensor.py
index b595ffe..2d570db 100644
--- a/varipeps/peps/tensor.py
+++ b/varipeps/peps/tensor.py
@@ -1103,3 +1103,738 @@ def tree_unflatten(
             max_chi=max_chi,
             sanity_checks=False,
         )
+
+
+@dataclass(frozen=True)
+@register_pytree_node_class
+class PEPS_Tensor_Structure_Factor(PEPS_Tensor):
+    """
+    Class to model a single a PEPS tensor with the corresponding CTM tensors.
+
+    Args:
+      tensor (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        PEPS tensor
+      C1 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        C1 tensor
+      C2 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        C2 tensor
+      C3 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        C3 tensor
+      C4 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        C4 tensor
+      T1 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        T1 tensor
+      T2 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        T2 tensor
+      T3 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        T3 tensor
+      T4 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        T4 tensor
+      C1_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        C1 tensor including structure factor phase
+      C2_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        C2 tensor including structure factor phase
+      C3_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        C3 tensor including structure factor phase
+      C4_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        C4 tensor including structure factor phase
+      T1_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        T1 tensor including structure factor phase
+      T2_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        T2 tensor including structure factor phase
+      T3_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        T3 tensor including structure factor phase
+      T4_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+        T4 tensor including structure factor phase
+      d (:obj:`int`):
+        Physical dimension of the PEPS tensor
+      D (:term:`sequence` of :obj:`int`):
+        Sequence of the bond dimensions of the PEPS tensor
+      chi (:obj:`int`):
+        Bond dimension for the CTM tensors
+      max_chi (:obj:`int`):
+        Maximal allowed bond dimension of environment tensors.
+    """
+
+    C1_phase: Tensor = None
+    C2_phase: Tensor = None
+    C3_phase: Tensor = None
+    C4_phase: Tensor = None
+
+    T1_phase: Tensor = None
+    T2_phase: Tensor = None
+    T3_phase: Tensor = None
+    T4_phase: Tensor = None
+
+    def __post_init__(self) -> None:
+        super().__post_init__()
+
+        if not (
+            self.T1_phase.shape[1] == self.T1_phase.shape[2] == self.D[3]
+            and self.T2_phase.shape[0] == self.T2_phase.shape[1] == self.D[2]
+            and self.T3_phase.shape[2] == self.T3_phase.shape[3] == self.D[1]
+            and self.T4_phase.shape[1] == self.T4_phase.shape[2] == self.D[0]
+        ):
+            raise ValueError(
+                "At least one transfer tensors mismatch bond dimensions of PEPS tensor."
+            )
+
+    @classmethod
+    def from_tensor(
+        cls: Type[T_PEPS_Tensor],
+        tensor: Tensor,
+        d: int,
+        D: Union[int, Sequence[int]],
+        chi: int,
+        max_chi: Optional[int] = None,
+        *,
+        ctm_tensors_are_identities: bool = True,
+        normalize: bool = True,
+        seed: Optional[int] = None,
+        backend: str = "jax",
+    ) -> T_PEPS_Tensor:
+        """
+        Initialize a PEPS tensor object with a given tensor and new CTM tensors.
+
+        Args:
+          tensor (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            PEPS tensor to initialize the object with
+          d (:obj:`int`):
+            Physical dimension
+          D (:obj:`int` or :term:`sequence` of :obj:`int`):
+            Bond dimensions for the PEPS tensor
+          chi (:obj:`int`):
+            Bond dimension for the environment tensors
+          max_chi (:obj:`int`):
+            Maximal allowed bond dimension for the environment tensors
+        Keyword args:
+          ctm_tensors_are_identities (:obj:`bool`, optional):
+            Flag if the CTM tensors are initialized as identities. Otherwise,
+            they are initialized randomly. Defaults to True.
+          normalize (:obj:`bool`, optional):
+            Flag if the generated tensors are normalized. Defaults to True.
+          seed (:obj:`int`, optional):
+            Seed for the random number generator.
+          backend (:obj:`str`, optional):
+            Backend for the generated tensors (may be ``jax`` or ``numpy``).
+            Defaults to ``jax``.
+        Returns:
+          PEPS_Tensor:
+            Instance of PEPS_Tensor with the randomly initialized tensors.
+        """
+        if not is_tensor(tensor):
+            raise ValueError("Invalid argument for tensor.")
+
+        if isinstance(D, int):
+            D = (D,) * 4
+        elif isinstance(D, collections.abc.Sequence) and not isinstance(D, tuple):
+            D = tuple(D)
+
+        if not all(isinstance(i, int) for i in D) or not len(D) == 4:
+            raise ValueError("Invalid argument for D.")
+
+        if (
+            tensor.shape[0] != D[0]
+            or tensor.shape[1] != D[1]
+            or tensor.shape[3] != D[2]
+            or tensor.shape[4] != D[3]
+            or tensor.shape[2] != d
+        ):
+            raise ValueError("Tensor dimensions mismatch the dimension arguments.")
+
+        if max_chi is None:
+            max_chi = chi
+
+        dtype = tensor.dtype
+
+        if ctm_tensors_are_identities:
+            C1 = jnp.ones((1, 1), dtype=dtype)
+            C2 = jnp.ones((1, 1), dtype=dtype)
+            C3 = jnp.ones((1, 1), dtype=dtype)
+            C4 = jnp.ones((1, 1), dtype=dtype)
+
+            T1 = jnp.eye(D[3], dtype=dtype).reshape(1, D[3], D[3], 1)
+            T2 = jnp.eye(D[2], dtype=dtype).reshape(D[2], D[2], 1, 1)
+            T3 = jnp.eye(D[1], dtype=dtype).reshape(1, 1, D[1], D[1])
+            T4 = jnp.eye(D[0], dtype=dtype).reshape(1, D[0], D[0], 1)
+
+            C1_phase = jnp.ones((1, 1), dtype=dtype)
+            C2_phase = jnp.ones((1, 1), dtype=dtype)
+            C3_phase = jnp.ones((1, 1), dtype=dtype)
+            C4_phase = jnp.ones((1, 1), dtype=dtype)
+
+            T1_phase = jnp.eye(D[3], dtype=dtype).reshape(1, D[3], D[3], 1)
+            T2_phase = jnp.eye(D[2], dtype=dtype).reshape(D[2], D[2], 1, 1)
+            T3_phase = jnp.eye(D[1], dtype=dtype).reshape(1, 1, D[1], D[1])
+            T4_phase = jnp.eye(D[0], dtype=dtype).reshape(1, D[0], D[0], 1)
+        else:
+            rng = PEPS_Random_Number_Generator.get_generator(seed, backend=backend)
+
+            C1 = rng.block((chi, chi), dtype, normalize=normalize)
+            C2 = rng.block((chi, chi), dtype, normalize=normalize)
+            C3 = rng.block((chi, chi), dtype, normalize=normalize)
+            C4 = rng.block((chi, chi), dtype, normalize=normalize)
+
+            T1 = rng.block((chi, D[3], D[3], chi), dtype, normalize=normalize)
+            T2 = rng.block((D[2], D[2], chi, chi), dtype, normalize=normalize)
+            T3 = rng.block((chi, chi, D[1], D[1]), dtype, normalize=normalize)
+            T4 = rng.block((chi, D[0], D[0], chi), dtype, normalize=normalize)
+
+            C1_phase = rng.block((chi, chi), dtype, normalize=normalize)
+            C2_phase = rng.block((chi, chi), dtype, normalize=normalize)
+            C3_phase = rng.block((chi, chi), dtype, normalize=normalize)
+            C4_phase = rng.block((chi, chi), dtype, normalize=normalize)
+
+            T1_phase = rng.block((chi, D[3], D[3], chi), dtype, normalize=normalize)
+            T2_phase = rng.block((D[2], D[2], chi, chi), dtype, normalize=normalize)
+            T3_phase = rng.block((chi, chi, D[1], D[1]), dtype, normalize=normalize)
+            T4_phase = rng.block((chi, D[0], D[0], chi), dtype, normalize=normalize)
+
+        return cls(
+            tensor=tensor,
+            C1=C1,
+            C2=C2,
+            C3=C3,
+            C4=C4,
+            T1=T1,
+            T2=T2,
+            T3=T3,
+            T4=T4,
+            C1_phase=C1_phase,
+            C2_phase=C2_phase,
+            C3_phase=C3_phase,
+            C4_phase=C4_phase,
+            T1_phase=T1_phase,
+            T2_phase=T2_phase,
+            T3_phase=T3_phase,
+            T4_phase=T4_phase,
+            d=d,
+            D=D,  # type: ignore
+            chi=chi,
+            max_chi=max_chi,
+        )
+
+    def change_chi(
+        self: T_PEPS_Tensor,
+        new_chi: int,
+        *,
+        reinitialize_env_as_identities: bool = True,
+    ) -> T_PEPS_Tensor:
+        """
+        Change the environment bond dimension and returns new object of the class.
+
+        Args:
+          new_chi (:obj:`int`):
+            New value for environment bond dimension.
+        Keyword args:
+          reinitialize_env_as_identities (:obj:`bool`):
+            Reinitialize the CTM tensors as identities if decreasing the dimension.
+        Returns:
+          :obj:`~varipeps.peps.PEPS_Tensor`:
+            New instance of the class with the increased value.
+        """
+        if new_chi > self.max_chi:
+            raise ValueError(
+                "Increase above the max value for environment bond dimension."
+            )
+
+        if new_chi < self.chi and reinitialize_env_as_identities:
+            return type(self)(
+                tensor=self.tensor,
+                C1=jnp.ones((1, 1), dtype=self.C1.dtype),
+                C2=jnp.ones((1, 1), dtype=self.C2.dtype),
+                C3=jnp.ones((1, 1), dtype=self.C3.dtype),
+                C4=jnp.ones((1, 1), dtype=self.C4.dtype),
+                T1=jnp.eye(self.D[3], dtype=self.T1.dtype).reshape(
+                    1, self.D[3], self.D[3], 1
+                ),
+                T2=jnp.eye(self.D[2], dtype=self.T2.dtype).reshape(
+                    self.D[2], self.D[2], 1, 1
+                ),
+                T3=jnp.eye(self.D[1], dtype=self.T3.dtype).reshape(
+                    1, 1, self.D[1], self.D[1]
+                ),
+                T4=jnp.eye(self.D[0], dtype=self.T4.dtype).reshape(
+                    1, self.D[0], self.D[0], 1
+                ),
+                C1_phase=jnp.ones((1, 1), dtype=self.C1_phase.dtype),
+                C2_phase=jnp.ones((1, 1), dtype=self.C2_phase.dtype),
+                C3_phase=jnp.ones((1, 1), dtype=self.C3_phase.dtype),
+                C4_phase=jnp.ones((1, 1), dtype=self.C4_phase.dtype),
+                T1_phase=jnp.eye(self.D[3], dtype=self.T1_phase.dtype).reshape(
+                    1, self.D[3], self.D[3], 1
+                ),
+                T2_phase=jnp.eye(self.D[2], dtype=self.T2_phase.dtype).reshape(
+                    self.D[2], self.D[2], 1, 1
+                ),
+                T3_phase=jnp.eye(self.D[1], dtype=self.T3_phase.dtype).reshape(
+                    1, 1, self.D[1], self.D[1]
+                ),
+                T4_phase=jnp.eye(self.D[0], dtype=self.T4_phase.dtype).reshape(
+                    1, self.D[0], self.D[0], 1
+                ),
+                d=self.d,
+                D=self.D,
+                chi=new_chi,
+                max_chi=self.max_chi,
+            )
+        else:
+            return type(self)(
+                tensor=self.tensor,
+                C1=self.C1,
+                C2=self.C2,
+                C3=self.C3,
+                C4=self.C4,
+                T1=self.T1,
+                T2=self.T2,
+                T3=self.T3,
+                T4=self.T4,
+                C1_phase=self.C1_phase,
+                C2_phase=self.C2_phase,
+                C3_phase=self.C3_phase,
+                C4_phase=self.C4_phase,
+                T1_phase=self.T1_phase,
+                T2_phase=self.T2_phase,
+                T3_phase=self.T3_phase,
+                T4_phase=self.T4_phase,
+                d=self.d,
+                D=self.D,
+                chi=new_chi,
+                max_chi=self.max_chi,
+            )
+
+    def increase_max_chi(
+        self: T_PEPS_Tensor,
+        new_max_chi: int,
+    ) -> T_PEPS_Tensor:
+        """
+        Change the maximal environment bond dimension and returns new object of the class.
+
+        Args:
+          new_max_chi (:obj:`int`):
+            New value for maximal environment bond dimension.
+        Returns:
+          :obj:`~varipeps.peps.PEPS_Tensor`:
+            New instance of the class with the increased value.
+        """
+        if new_max_chi < self.max_chi:
+            raise ValueError(
+                "Decrease below the old max value for environment bond dimension."
+            )
+
+        return type(self)(
+            tensor=self.tensor,
+            C1=self.C1,
+            C2=self.C2,
+            C3=self.C3,
+            C4=self.C4,
+            T1=self.T1,
+            T2=self.T2,
+            T3=self.T3,
+            T4=self.T4,
+            C1_phase=self.C1_phase,
+            C2_phase=self.C2_phase,
+            C3_phase=self.C3_phase,
+            C4_phase=self.C4_phase,
+            T1_phase=self.T1_phase,
+            T2_phase=self.T2_phase,
+            T3_phase=self.T3_phase,
+            T4_phase=self.T4_phase,
+            d=self.d,
+            D=self.D,
+            chi=self.chi,
+            max_chi=new_max_chi,
+        )
+
+    def replace_left_env_tensors(
+        self: T_PEPS_Tensor,
+        new_C1: Tensor,
+        new_T4: Tensor,
+        new_C4: Tensor,
+        new_C1_phase: Tensor,
+        new_T4_phase: Tensor,
+        new_C4_phase: Tensor,
+    ) -> T_PEPS_Tensor:
+        """
+        Replace the left CTMRG tensors and returns new object of the class.
+
+        Args:
+          new_C1 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C1 tensor.
+          new_T4 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New T4 tensor.
+          new_C4 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C4 tensor.
+          new_C1_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C1 tensor including structure factor phase.
+          new_T4_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New T4 tensor including structure factor phase.
+          new_C4_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C4 tensor including structure factor phase.
+        Returns:
+          :obj:`~varipeps.peps.PEPS_Tensor`:
+            New instance of the class with the tensors replaced.
+        """
+        return type(self)(
+            tensor=self.tensor,
+            C1=new_C1,
+            C2=self.C2,
+            C3=self.C3,
+            C4=new_C4,
+            T1=self.T1,
+            T2=self.T2,
+            T3=self.T3,
+            T4=new_T4,
+            C1_phase=new_C1_phase,
+            C2_phase=self.C2_phase,
+            C3_phase=self.C3_phase,
+            C4_phase=new_C4_phase,
+            T1_phase=self.T1_phase,
+            T2_phase=self.T2_phase,
+            T3_phase=self.T3_phase,
+            T4_phase=new_T4_phase,
+            d=self.d,
+            D=self.D,
+            chi=self.chi,
+            max_chi=self.max_chi,
+        )
+
+    def replace_right_env_tensors(
+        self: T_PEPS_Tensor,
+        new_C2: Tensor,
+        new_T2: Tensor,
+        new_C3: Tensor,
+        new_C2_phase: Tensor,
+        new_T2_phase: Tensor,
+        new_C3_phase: Tensor,
+    ) -> T_PEPS_Tensor:
+        """
+        Replace the right CTMRG tensors and returns new object of the class.
+
+        Args:
+          new_C2 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C2 tensor.
+          new_T2 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New T2 tensor.
+          new_C3 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C3 tensor.
+          new_C2_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C2 tensor including structure factor phase.
+          new_T2_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New T2 tensor including structure factor phase.
+          new_C3_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C3 tensor including structure factor phase.
+        Returns:
+          :obj:`~varipeps.peps.PEPS_Tensor`:
+            New instance of the class with the tensors replaced.
+        """
+        return type(self)(
+            tensor=self.tensor,
+            C1=self.C1,
+            C2=new_C2,
+            C3=new_C3,
+            C4=self.C4,
+            T1=self.T1,
+            T2=new_T2,
+            T3=self.T3,
+            T4=self.T4,
+            C1_phase=self.C1_phase,
+            C2_phase=new_C2_phase,
+            C3_phase=new_C3_phase,
+            C4_phase=self.C4_phase,
+            T1_phase=self.T1_phase,
+            T2_phase=new_T2_phase,
+            T3_phase=self.T3_phase,
+            T4_phase=self.T4_phase,
+            d=self.d,
+            D=self.D,
+            chi=self.chi,
+            max_chi=self.max_chi,
+        )
+
+    def replace_top_env_tensors(
+        self: T_PEPS_Tensor,
+        new_C1: Tensor,
+        new_T1: Tensor,
+        new_C2: Tensor,
+        new_C1_phase: Tensor,
+        new_T1_phase: Tensor,
+        new_C2_phase: Tensor,
+    ) -> T_PEPS_Tensor:
+        """
+        Replace the top CTMRG tensors and returns new object of the class.
+
+        Args:
+          new_C1 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C1 tensor.
+          new_T1 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New T1 tensor.
+          new_C2 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C2 tensor.
+          new_C1_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C1 tensor including structure factor phase.
+          new_T1_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New T1 tensor including structure factor phase.
+          new_C2_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C2 tensor including structure factor phase.
+        Returns:
+          :obj:`~varipeps.peps.PEPS_Tensor`:
+            New instance of the class with the tensors replaced.
+        """
+        return type(self)(
+            tensor=self.tensor,
+            C1=new_C1,
+            C2=new_C2,
+            C3=self.C3,
+            C4=self.C4,
+            T1=new_T1,
+            T2=self.T2,
+            T3=self.T3,
+            T4=self.T4,
+            C1_phase=new_C1_phase,
+            C2_phase=new_C2_phase,
+            C3_phase=self.C3_phase,
+            C4_phase=self.C4_phase,
+            T1_phase=new_T1_phase,
+            T2_phase=self.T2_phase,
+            T3_phase=self.T3_phase,
+            T4_phase=self.T4_phase,
+            d=self.d,
+            D=self.D,
+            chi=self.chi,
+            max_chi=self.max_chi,
+        )
+
+    def replace_bottom_env_tensors(
+        self: T_PEPS_Tensor,
+        new_C4: Tensor,
+        new_T3: Tensor,
+        new_C3: Tensor,
+        new_C4_phase: Tensor,
+        new_T3_phase: Tensor,
+        new_C3_phase: Tensor,
+    ) -> T_PEPS_Tensor:
+        """
+        Replace the bottom CTMRG tensors and returns new object of the class.
+
+        Args:
+          new_C4 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C4 tensor.
+          new_T3 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New T3 tensor.
+          new_C3 (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C3 tensor.
+          new_C4_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C4 tensor including structure factor phase.
+          new_T3_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New T3 tensor including structure factor phase.
+          new_C3_phase (:obj:`numpy.ndarray` or :obj:`jax.numpy.ndarray`):
+            New C3 tensor including structure factor phase.
+        Returns:
+          :obj:`~varipeps.peps.PEPS_Tensor`:
+            New instance of the class with the tensors replaced.
+        """
+        return type(self)(
+            tensor=self.tensor,
+            C1=self.C1,
+            C2=self.C2,
+            C3=new_C3,
+            C4=new_C4,
+            T1=self.T1,
+            T2=self.T2,
+            T3=new_T3,
+            T4=self.T4,
+            C1_phase=self.C1_phase,
+            C2_phase=self.C2_phase,
+            C3_phase=new_C3_phase,
+            C4_phase=new_C4_phase,
+            T1_phase=self.T1_phase,
+            T2_phase=self.T2_phase,
+            T3_phase=new_T3_phase,
+            T4_phase=self.T4_phase,
+            d=self.d,
+            D=self.D,
+            chi=self.chi,
+            max_chi=self.max_chi,
+        )
+
+    def save_to_group(self, grp: h5py.Group) -> None:
+        """
+        Store the PEPS tensor into a HDF5 group.
+
+        Args:
+          grp (:obj:`h5py.Group`):
+            HDF5 group object to save the data into.
+        """
+        grp.attrs["d"] = self.d
+        grp.attrs["D"] = self.D
+        grp.attrs["chi"] = self.chi
+        grp.attrs["max_chi"] = self.max_chi
+        grp.create_dataset(
+            "tensor", data=self.tensor, compression="gzip", compression_opts=6
+        )
+        grp.create_dataset("C1", data=self.C1, compression="gzip", compression_opts=6)
+        grp.create_dataset("C2", data=self.C2, compression="gzip", compression_opts=6)
+        grp.create_dataset("C3", data=self.C3, compression="gzip", compression_opts=6)
+        grp.create_dataset("C4", data=self.C4, compression="gzip", compression_opts=6)
+        grp.create_dataset("T1", data=self.T1, compression="gzip", compression_opts=6)
+        grp.create_dataset("T2", data=self.T2, compression="gzip", compression_opts=6)
+        grp.create_dataset("T3", data=self.T3, compression="gzip", compression_opts=6)
+        grp.create_dataset("T4", data=self.T4, compression="gzip", compression_opts=6)
+        grp.create_dataset(
+            "C1_phase", data=self.C1_phase, compression="gzip", compression_opts=6
+        )
+        grp.create_dataset(
+            "C2_phase", data=self.C2_phase, compression="gzip", compression_opts=6
+        )
+        grp.create_dataset(
+            "C3_phase", data=self.C3_phase, compression="gzip", compression_opts=6
+        )
+        grp.create_dataset(
+            "C4_phase", data=self.C4_phase, compression="gzip", compression_opts=6
+        )
+        grp.create_dataset(
+            "T1_phase", data=self.T1_phase, compression="gzip", compression_opts=6
+        )
+        grp.create_dataset(
+            "T2_phase", data=self.T2_phase, compression="gzip", compression_opts=6
+        )
+        grp.create_dataset(
+            "T3_phase", data=self.T3_phase, compression="gzip", compression_opts=6
+        )
+        grp.create_dataset(
+            "T4_phase", data=self.T4_phase, compression="gzip", compression_opts=6
+        )
+
+    @classmethod
+    def load_from_group(cls: Type[T_PEPS_Tensor], grp: h5py.Group) -> T_PEPS_Tensor:
+        """
+        Load the PEPS tensor from a HDF5 group.
+
+        Args:
+          grp (:obj:`h5py.Group`):
+            HDF5 group object to load the data from.
+        """
+        d = int(grp.attrs["d"])
+        D = tuple(int(i) for i in grp.attrs["D"])
+        chi = int(grp.attrs["chi"])
+        try:
+            max_chi = int(grp.attrs["max_chi"])
+        except KeyError:
+            max_chi = chi
+
+        tensor = jnp.asarray(grp["tensor"])
+        C1 = jnp.asarray(grp["C1"])
+        C2 = jnp.asarray(grp["C2"])
+        C3 = jnp.asarray(grp["C3"])
+        C4 = jnp.asarray(grp["C4"])
+        T1 = jnp.asarray(grp["T1"])
+        T2 = jnp.asarray(grp["T2"])
+        T3 = jnp.asarray(grp["T3"])
+        T4 = jnp.asarray(grp["T4"])
+        C1_phase = jnp.asarray(grp["C1_phase"])
+        C2_phase = jnp.asarray(grp["C2_phase"])
+        C3_phase = jnp.asarray(grp["C3_phase"])
+        C4_phase = jnp.asarray(grp["C4_phase"])
+        T1_phase = jnp.asarray(grp["T1_phase"])
+        T2_phase = jnp.asarray(grp["T2_phase"])
+        T3_phase = jnp.asarray(grp["T3_phase"])
+        T4_phase = jnp.asarray(grp["T4_phase"])
+
+        return cls(
+            tensor=tensor,
+            C1=C1,
+            C2=C2,
+            C3=C3,
+            C4=C4,
+            T1=T1,
+            T2=T2,
+            T3=T3,
+            T4=T4,
+            C1_phase=C1_phase,
+            C2_phase=C2_phase,
+            C3_phase=C3_phase,
+            C4_phase=C4_phase,
+            T1_phase=T1_phase,
+            T2_phase=T2_phase,
+            T3_phase=T3_phase,
+            T4_phase=T4_phase,
+            d=d,
+            D=D,
+            chi=chi,
+            max_chi=max_chi,
+        )
+
+    def tree_flatten(self) -> Tuple[Tuple[Any, ...], Tuple[Any, ...]]:
+        data = (
+            self.tensor,
+            self.C1,
+            self.C2,
+            self.C3,
+            self.C4,
+            self.T1,
+            self.T2,
+            self.T3,
+            self.T4,
+            self.C1_phase,
+            self.C2_phase,
+            self.C3_phase,
+            self.C4_phase,
+            self.T1_phase,
+            self.T2_phase,
+            self.T3_phase,
+            self.T4_phase,
+        )
+        aux_data = (self.d, self.D, self.chi, self.max_chi)
+
+        return (data, aux_data)
+
+    @classmethod
+    def tree_unflatten(
+        cls: Type[T_PEPS_Tensor], aux_data: Tuple[Any, ...], children: Tuple[Any, ...]
+    ) -> T_PEPS_Tensor:
+        (
+            tensor,
+            C1,
+            C2,
+            C3,
+            C4,
+            T1,
+            T2,
+            T3,
+            T4,
+            C1_phase,
+            C2_phase,
+            C3_phase,
+            C4_phase,
+            T1_phase,
+            T2_phase,
+            T3_phase,
+            T4_phase,
+        ) = children
+        d, D, chi, max_chi = aux_data
+
+        return cls(
+            tensor=tensor,
+            C1=C1,
+            C2=C2,
+            C3=C3,
+            C4=C4,
+            T1=T1,
+            T2=T2,
+            T3=T3,
+            T4=T4,
+            C1_phase=C1_phase,
+            C2_phase=C2_phase,
+            C3_phase=C3_phase,
+            C4_phase=C4_phase,
+            T1_phase=T1_phase,
+            T2_phase=T2_phase,
+            T3_phase=T3_phase,
+            T4_phase=T4_phase,
+            d=d,
+            D=D,
+            chi=chi,
+            max_chi=max_chi,
+            sanity_checks=False,
+        )