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Physica Scripta

Generalized Hartree-Fock to phase transition

Stella M. Peltier

Published Jun 1, 1992• 0 citations
Publisher

Abstract

For the description of the superconducting phase transition in a manyfermion system, the constrained Hartree-Fock theory with pairing correlations is explored. The influence of pairing on binding energies and critical values is discussed for the ground state of the generalized pseudospin model. Critical pure-pairing interaction coincides with that of the exact case.

DOI
10.1088/0031-8949/45/6/001

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For the description of the superconducting phase transition in a manyfermion system, the constrained Hartree-Fock theory with pairing correlations is explored. The influence of pairing on binding energies and critical values is discussed for the ground state of the generalized pseudospin model. Critical pure-pairing interaction coincides with that of the exact case.
To describe comprehensively the superconducting phase together with the other phases realized in the copper oxcides, the normal phase, the antiferro-magnetic and the spin-glass phases, an application of the constrained thermal Hartree-Fock-Bogoliubov (CTHFB) approximation is proposed. A set of the electron number- and the magnetization-constrained formalism is exemplified by employing the one-band Hubbard model. The CTHFB equation is applicable to the microscopic interaction whether it includes the phonon-mediated pairing interaction, or it provides a self-sustaining mechanism of the Cooper pair formation. A new type of the order parameter is introduced by extending the generalized Bogoliubov transformation to mix electron spin projections onto the quantization axis (i.e. S^z\hat{S}_{z}S^z​). This yields the lowered minimum of the grand potential, which corresponds to the physical solution violating time-reversal invariance. The gradient method is proposed to solve the CTHFB equation, the non-linear eigenvalue broblem with constraints.
We present a theorem on total pseudospin as an eigenvalue in a state. The total pseudospin is determined by the summation of the phase factors, written in terms of pseudospin operator and number of electrons. We discuss its relation with \ensuremath{\eta}-pairing superconductivity and ground-state energy level ordering of a system with pseudospin symmetry. Finally as an application of the theorem we show that the ground state of a generalized Hubbard model is superconducting for any electron filling. \textcopyright{} 1996 The American Physical Society.
The Hartree-Fock theory for many fermions with plane-wave orbitals but with abnormal occupation is studied. A one-dimensional problem with an interparticle interaction of finite range which saturates the NNN body system at a fixed density and finite binding energy is solved explicitly. A direct variation of the resulting Hartree-Fock energy with respect to the additional variational parameters introduced is carried out numerically and results reminiscent of a gas-to-liquid phase transition are found.NUCLEAR STRUCTURE plane-wave Hartree-Fock; model calculation; nuclear matter.
The extended Hubbard model with the pair-hopping interaction, i.e. the Penson-Kolb-Hubbard model, is one of the conceptually simplest phenomenological models for studying correlations and for description of superconductivity in very narrow-band systems with short-range, almost unretarded pairing.We present ground state phase diagrams of the model derived within the broken-symmetry Hartree-Fock approximation in the narrow-bandwidth regime and compare these results with the exact ones in the atomic limit for the limit of high dimensions.The investigation of the diagrams of the model show that results obtained within both approaches are consistent, although for the case of the finite single-electron hopping phases with magnetic long-range order also occur.
The importance of ground-state correlations in the spectroscopy of a finite many-particle system, such as the nucleus, is investigated for the model Hamiltonian of Lipkin, Meshkov, and Glick. In particular, we have investigated their effect on the solution of the equations of motion for excitation energies, transition matrix elements, and the correlation energy of the ground state. Methods are studied for calculating the correlations needed to make the necessary corrections to the equations of motion. Also studied is the behavior, with increase of interaction strength, of the phase transition from the spherical to the strongly deformed intrinsic states, in the projected Hartree-Fock scheme.