Papers by Aranya Bhattacharya
Journal of High Energy Physics, Dec 14, 2021
We compute the holographic subregion complexity of a radiation subsystem in a geometric secret-sh... more We compute the holographic subregion complexity of a radiation subsystem in a geometric secret-sharing model of Hawking radiation in the "complexity = volume" proposal. The model is constructed using multiboundary wormhole geometries in AdS 3. The entanglement curve for secret-sharing captures a crossover between two minimal curves in the geometry apart from the usual eternal Page curve present for the complete radiation entanglement. We compute the complexity dual to the secret-sharing minimal surfaces and study their "time" evolution. When we have access to a small part of the radiation, the complexity shows a jump at the secret-sharing time larger than the Page time. Moreover, the minimal surfaces do not have access to the entire island region for this particular case. They can only access it partially. We describe this inaccessibility in the context of "classical" Markov recovery.
Physical review, Oct 14, 2022
We compute the pseudocomplexity of purification corresponding to the reduced transition matrices ... more We compute the pseudocomplexity of purification corresponding to the reduced transition matrices for free scalar field theories with an arbitrary dynamical exponent. We plot the behavior of complexity with various parameters of the theory under study and compare it with the complexity of purification of the reduced density matrices of the two states jψ 1 i and jψ 2 i that constitute the transition matrix. We first find the transition matrix by reducing to a small number (1 and 2) of degrees of freedom in lattice from a lattice system with many lattice points and then purify it by doubling the degrees of freedom (2 and 4 respectively) for this reduced system. This is a primary step towards the natural extension to the idea of the complexity of purification for reduced density matrices relevant for the studies related to postselection.
arXiv (Cornell University), Mar 7, 2023
Continuing the previous initiatives [1, 2], we pursue the exploration of operator growth and Kryl... more Continuing the previous initiatives [1, 2], we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm generating two bi-orthogonal Krylov spaces, which individually generate non-orthogonal subspaces. Unlike the previously studied Arnoldi iteration, this algorithm renders the Lindbladian into a purely tridiagonal form, thus opening up a possibility to study a wide class of dissipative integrable and chaotic systems by computing Krylov complexity at late times. Our study relies on two specific systems, the dissipative transverse-field Ising model (TFIM) and the dissipative interacting XXZ chain. We find that, for the weak coupling, initial Lanczos coefficients can efficiently distinguish integrable and chaotic evolution before the dissipative effect sets in, which results in more fluctuations in higher Lanczos coefficients. This results in the equal saturation of late-time complexity for both integrable and chaotic cases, making the notion of late-time chaos dubious.
arXiv (Cornell University), Jul 25, 2023
We compute the complexity for the mixed state density operator derived from a onedimensional disc... more We compute the complexity for the mixed state density operator derived from a onedimensional discrete-time quantum walk (DTQW). The complexity is computed using a 2-qubit quantum circuit obtained from canonically purifying the mixed state. We demonstrate that the Nielson complexity for the unitary evolution oscillates around a mean circuit depth of k. Further, the complexity of the step-wise evolution operator grows cumulatively and linearly with the steps. From a quantum circuit perspective, this implies a succession of circuits of (near) constant depth to be applied to reach the final state.
arXiv (Cornell University), Apr 19, 2023
Recently, it has been argued in [1] that Jackiw-Teitelboim (JT) gravity can be naturally realized... more Recently, it has been argued in [1] that Jackiw-Teitelboim (JT) gravity can be naturally realized in the Karch-Randall braneworld in (2 + 1) dimensions. Using the 'complexity=volume' proposal, we studied this model and computed the holographic complexity of the JT gravity from the bulk perspective. We find that the complexity grows linearly with boundary time at late times, and the leading order contribution is proportional to the φ 0 , similar to the answer found in [2]. However, in addition, we find subleading corrections to the complexity solely arising from the fluctuations of these Karch-Randall branes.
Physical review, Aug 17, 2020
The holographic duals of entanglement of purification (EoP) through the entanglement wedge cross ... more The holographic duals of entanglement of purification (EoP) through the entanglement wedge cross section (EWCS) have been a well-discussed topic in the literature recently. More general entanglement measures involving multipartite information and their holographic duals have also been proposed. On the other hand, the recent program reproducing the Page curve in black hole entropy with the notion of islands has also been an intriguing area of interest. A toy model involving multiboundary wormholes in AdS 3 was able to capture many interesting facts about such calculations. In such a toy model, the notion of islands was intuitively connected to quantum error correction. We try to bridge the ideas of the two programs, especially in AdS 3 =CFT 2 , and give a description of the islands in terms of multipartite entanglement of purification. This clarifies a few simplified assumptions made while describing the toy model and also enables us to understand the familiar information paradox within the framework of the same model.
Journal of High Energy Physics, May 1, 2021
We study the entanglement islands and subsystem volume complexity corresponding to the left/ righ... more We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in d-dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.
arXiv (Cornell University), Mar 26, 2020
The holographic duals of Entanglement of Purification through the Entanglement Wedge Cross Sectio... more The holographic duals of Entanglement of Purification through the Entanglement Wedge Cross Section has been a well-discussed topic in the literature recently. More general entanglement measures involving multipartite information and their holographic duals have also been discovered in this line of study. On the other hand, the recent intriguing program deriving the Page Curve in Black hole entropy using the notion of islands has made a good amount of progress. A toy model involving Multiboundary wormholes in AdS$_{3}$ has been able to capture many interesting ideas about such calculations. In such a toy model, the notion of islands has been intuitively connected to quantum error correction. We try to bridge the ideas of the two programs especially in AdS$_{3}$/CFT$_{2}$ and give a description of the islands in terms of multipartite entanglement of purification. This clarifies a few simplified assumptions made while describing the toy model and also enables us to understand the familiar information paradox within the framework of the same model without constructing any new parallel model including baby universes.
Journal of High Energy Physics, Jul 1, 2021
Introduction of electric field in the D-brane worldvolume induces a horizon in the open string ge... more Introduction of electric field in the D-brane worldvolume induces a horizon in the open string geometry perceived by the brane fluctuations. We study the holographic entanglement entropy (HEE) and subregion complexity (HSC) in these asymptotically AdS geometries in three, four and five dimensions aiming to capture these quantities in the flavor sector introduced by the D-branes. Both the strip and spherical subregions have been considered. We show that the Bekenstein-Hawking entropy associated with the open string horizon, which earlier failed to reproduce the thermal entropy in the boundary, now precisely matches with the entanglement entropy at high temperatures. We check the validity of embedding function theorem while computing the HEE and attempt to reproduce the first law of entanglement thermodynamics, at least at leading order. On the basis of obtained results, we also reflect upon consequences of applying Ryu-Takayanagi proposal on these non-Einstein geometries.
Journal of High Energy Physics, Dec 14, 2022
Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construct... more Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.
Physical review, Mar 29, 2022
Considering a doubly holographic model, we study the evolution of holographic subregion complexit... more Considering a doubly holographic model, we study the evolution of holographic subregion complexity corresponding to deformations of bath state by a relevant scalar operator, which corresponds to a renormalization group flow from the AdS-Schwarzschild to the Kasner universe in the bulk. The subregion complexity shows a discontinuous jump at Page time at a fixed perturbation, where the discontinuity depends solely on the system's parameters. We show that the amount of discontinuity decreases with the perturbation as well as with the scaling dimension of the relevant scalar operator.
Journal of High Energy Physics
Recently, it has been argued in [1] that Jackiw-Teitelboim (JT) gravity can be naturally realized... more Recently, it has been argued in [1] that Jackiw-Teitelboim (JT) gravity can be naturally realized in the Karch-Randall braneworld in (2 + 1) dimensions. Using the ‘complexity=volume’ proposal, we studied this model and computed the holographic complexity of the JT gravity from the bulk perspective. We find that the complexity grows linearly with boundary time at late times, and the leading order contribution is proportional to the φ0, similar to the answer found in [2]. However, in addition, we find subleading corrections to the complexity solely arising from the fluctuations of these Karch-Randall branes.
arXiv (Cornell University), Apr 19, 2023
arXiv (Cornell University), Mar 7, 2023
arXiv (Cornell University), Jul 12, 2022
Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construct... more Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.
Journal of High Energy Physics
Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construct... more Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi i...
Physical Review D
We compute the pseudocomplexity of purification corresponding to the reduced transition matrices ... more We compute the pseudocomplexity of purification corresponding to the reduced transition matrices for free scalar field theories with an arbitrary dynamical exponent. We plot the behavior of complexity with various parameters of the theory under study and compare it with the complexity of purification of the reduced density matrices of the two states jψ 1 i and jψ 2 i that constitute the transition matrix. We first find the transition matrix by reducing to a small number (1 and 2) of degrees of freedom in lattice from a lattice system with many lattice points and then purify it by doubling the degrees of freedom (2 and 4 respectively) for this reduced system. This is a primary step towards the natural extension to the idea of the complexity of purification for reduced density matrices relevant for the studies related to postselection.
Like BPS D3 brane, the non-supersymmetric (non-susy) D3 brane of type IIB string theory is also k... more Like BPS D3 brane, the non-supersymmetric (non-susy) D3 brane of type IIB string theory is also known to have a decoupling limit and leads to a non-supersymmetric AdS/CFT correspondence. The throat geometry in this case represents a QFT which is neither conformal nor supersymmetric. The `black' version of the non-susy D3 brane in the decoupling limit describes a QFT at finite temperature. Here we first compute the entanglement entropy for small subsystem of such QFT from the decoupled geometry of `black' non-susy D3 brane using holographic technique. Then we study the entanglement thermodynamics for the weakly excited states of this QFT from the asymptotically AdS geometry of the decoupled `black' non-susy D3 brane. We observe that for small subsystem this background indeed satisfies a first law like relation with a universal (entanglement) temperature inversely proportional to the size of the subsystem and an (entanglement) pressure normal to the entangling surface. Fin...
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Papers by Aranya Bhattacharya