For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served... more For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.
We consider the widely adopted slave-boson method, which relies on a coherent-state functional-in... more We consider the widely adopted slave-boson method, which relies on a coherent-state functional-integral representation of the partition function and illustrate how to deal with the continuum imaginary time required by the very definition of the functional integral. We show that a correct treatment of the continuum limit of the functional integral modifies the free energy when fluctuation (1/N) corrections beyond
The three band Hubbard modal with nearest neighbour repulsion is studied in the U = c~ limit usin... more The three band Hubbard modal with nearest neighbour repulsion is studied in the U = c~ limit using the slave boson technique and the large N expansion. A charge transfer (CT) instability is found like ill weak coupling theory. The CT instability is always associated with a divergin 8 compressibility leading to a phase separation. The total density and CT susceptibilities are analysed in both the static and dynamic lindt to gain insight on the strong mixing between the density fluctuations and the excitonic modes. The evaluation to order ~ of the effective scattering amplitude in the Cooper channel shows the presence of superconducting instabilities in the s and d wave channel near the phase separation.
By reviewing the application of the renormalization group to different theoretical problems, we e... more By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given physical system. In particular, we show how the constraints due to the Ward identities, which implement the conservation laws associated with the various symmetries, help to minimize the number of independent running variables. This use of the Ward identities is examined both in the case of a stable phase and of a critical phenomenon. In the first case we consider effects to renormalizations of the Landau parameters. As a consequence, the occurrence of a metal-insulator transition is described as a critical breakdown of a Fermi liquid.
We derive a formula for the quantum corrections to the electrical current for a metal out of equi... more We derive a formula for the quantum corrections to the electrical current for a metal out of equilibrium. In the limit of linear current-voltage characteristics our formula reproduces the well known Altshuler-Aronov correction to the conductivity of a disordered metal. The current formula is obtained by a direct diagrammatic approach, and is shown to agree with what is obtained within the Keldysh formulation of the non-linear sigma model. As an application we calculate the current of a mesoscopic wire. We find a current-voltage characteristics that scales with eV /kT , and calculate the different scaling curves for a wire in the hot-electron regime and in the regime of full non-equilibrium.
For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served... more For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.
Spin-orbit interaction is usefully classified as extrinsic or intrinsic depending on its origin: ... more Spin-orbit interaction is usefully classified as extrinsic or intrinsic depending on its origin: the potential due to random impurities (extrinsic), or the crystalline potential associated with the band or device structure (intrinsic). In this paper we will show how by using a SU (2) formulation the two sources of spin-orbit interaction may be described in an elegant and unified way. As a result we obtain a simple description of the interplay of the two types of spin-orbit interaction, and a physically transparent explanation of the vanishing of the d.c. spin Hall conductivity in a Rashba two-dimensional electron gas when spin relaxation is neglected, and its reinstatement when spin relaxation is allowed. Furthermore, we obtain an explicit formula for the transverse spin polarization created by an electric current, which generalizes the standard formula obtained by Edelstein and Aronov and Lyanda-Geller by including extrinsic spin-orbit interaction and spin relaxation.
We analyze the ground-state properties of strongly-correlated electrons coupled with phonons by m... more We analyze the ground-state properties of strongly-correlated electrons coupled with phonons by means of a generalized Gutzwiller wavefunction which includes phononic degrees of freedom. We study in detail the paramagnetic half-filled Hubbard-Holstein model, where the electron-electron interaction can lead to a Mott transition, and the electron-phonon coupling to a bipolaronic transition. We critically discuss the quality of the proposed wavefunction in describing the various transitions and crossovers that occur as a function of the parameters. Previous variational attempts are recovered as particular choices of the wavefunction, while keeping all the variational freedom allows to access regions of the phase diagram otherwise inaccessible within previous variational approaches.
For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served... more For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.
We consider the widely adopted slave-boson method, which relies on a coherent-state functional-in... more We consider the widely adopted slave-boson method, which relies on a coherent-state functional-integral representation of the partition function and illustrate how to deal with the continuum imaginary time required by the very definition of the functional integral. We show that a correct treatment of the continuum limit of the functional integral modifies the free energy when fluctuation (1/N) corrections beyond
The three band Hubbard modal with nearest neighbour repulsion is studied in the U = c~ limit usin... more The three band Hubbard modal with nearest neighbour repulsion is studied in the U = c~ limit using the slave boson technique and the large N expansion. A charge transfer (CT) instability is found like ill weak coupling theory. The CT instability is always associated with a divergin 8 compressibility leading to a phase separation. The total density and CT susceptibilities are analysed in both the static and dynamic lindt to gain insight on the strong mixing between the density fluctuations and the excitonic modes. The evaluation to order ~ of the effective scattering amplitude in the Cooper channel shows the presence of superconducting instabilities in the s and d wave channel near the phase separation.
By reviewing the application of the renormalization group to different theoretical problems, we e... more By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given physical system. In particular, we show how the constraints due to the Ward identities, which implement the conservation laws associated with the various symmetries, help to minimize the number of independent running variables. This use of the Ward identities is examined both in the case of a stable phase and of a critical phenomenon. In the first case we consider effects to renormalizations of the Landau parameters. As a consequence, the occurrence of a metal-insulator transition is described as a critical breakdown of a Fermi liquid.
We derive a formula for the quantum corrections to the electrical current for a metal out of equi... more We derive a formula for the quantum corrections to the electrical current for a metal out of equilibrium. In the limit of linear current-voltage characteristics our formula reproduces the well known Altshuler-Aronov correction to the conductivity of a disordered metal. The current formula is obtained by a direct diagrammatic approach, and is shown to agree with what is obtained within the Keldysh formulation of the non-linear sigma model. As an application we calculate the current of a mesoscopic wire. We find a current-voltage characteristics that scales with eV /kT , and calculate the different scaling curves for a wire in the hot-electron regime and in the regime of full non-equilibrium.
For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served... more For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.
Spin-orbit interaction is usefully classified as extrinsic or intrinsic depending on its origin: ... more Spin-orbit interaction is usefully classified as extrinsic or intrinsic depending on its origin: the potential due to random impurities (extrinsic), or the crystalline potential associated with the band or device structure (intrinsic). In this paper we will show how by using a SU (2) formulation the two sources of spin-orbit interaction may be described in an elegant and unified way. As a result we obtain a simple description of the interplay of the two types of spin-orbit interaction, and a physically transparent explanation of the vanishing of the d.c. spin Hall conductivity in a Rashba two-dimensional electron gas when spin relaxation is neglected, and its reinstatement when spin relaxation is allowed. Furthermore, we obtain an explicit formula for the transverse spin polarization created by an electric current, which generalizes the standard formula obtained by Edelstein and Aronov and Lyanda-Geller by including extrinsic spin-orbit interaction and spin relaxation.
We analyze the ground-state properties of strongly-correlated electrons coupled with phonons by m... more We analyze the ground-state properties of strongly-correlated electrons coupled with phonons by means of a generalized Gutzwiller wavefunction which includes phononic degrees of freedom. We study in detail the paramagnetic half-filled Hubbard-Holstein model, where the electron-electron interaction can lead to a Mott transition, and the electron-phonon coupling to a bipolaronic transition. We critically discuss the quality of the proposed wavefunction in describing the various transitions and crossovers that occur as a function of the parameters. Previous variational attempts are recovered as particular choices of the wavefunction, while keeping all the variational freedom allows to access regions of the phase diagram otherwise inaccessible within previous variational approaches.
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Papers by R. Raimondi