Theory of the thermal single-determinant approximation

T. A. Kaplan, Petros N. Argyres

Tohru Ogawa

Pinhao Gu, So Hirata

Several closely related ab initio thermal mean-field theories for fermions, both well-established and new ones, are compared with one another at the formalism level and numerically. The theories considered are Fermi-Dirac theory; thermal Hartree-Fock (HF) theory; two modifications of the thermal single-determinant approximation of Kaplan and Argyres, Ann. Phys. 92, 1-24 (1975); and the first-order finite-temperature many-body perturbation theory based on a zero-temperature or thermal HF reference. Thermal full-configuration-interaction theory is used as the benchmark.

Pablo Ramos, Michele Pavanello

Over the years, several schemes have been proposed to describe multireference systems with Kohn-Sham Density Functional Theory. Problematic is the combination of two aspects: the Kohn-Sham reference wavefunction is usually taken to be a single Slater determinant, and approximate exchange-correlation functionals are typically derived form the local density approximation. In this work, we develop a theoretical framework that foregoes the single Slater determinant and instead employs thermal states as reference states for zero-temperature interacting systems. We provide convenient definitions of static and dynamic correlation functionals via an adiabatic connection approach. The formalism and computational results indicate that the entropic term of the thermal reference state is a good approximation to the static correlation functional. Hence, this work validates several reported results in the literature and motivates additional developments of static correlation density functionals.

Stella M. Peltier

Leo P. Kadanoff, Paul C. Martin

A fermion system with a simple attractive interaction is discussed with the aid of time-dependent correlation functions. Although perturbation theory is inapplicable, a sequence of correlation approximations described in the first paper of this series can be employed. The lowest approximation in the sequence expresses the two-particle correlation function in terms of single-particle functions and leads to the Hartree approximation; the second expresses three-particle correlation function in terms of one- and two-particle correlation functions and leads to the time-dependent correlation functions that characterize the super-conducting model of Bardeen, Cooper, and Schrieffer. In the second section of this paper these correlation functions are determined and the thermodynamic properties of the superconductor are calculated from them.In the third section of the paper, the electromagnetic effects of the superconductor predicted by the Bardeen-Cooper-Schrieffer time-dependent correlation functions are considered. Their unsatisfactory description of current conservation is indicated and overcome in the fourth section by a more accurate solution valid at nonvanishing temperature. This solution predicts different diffusive properties but the same Meissner effect and superconductive behavior, since the longitudinal current correlation function is modified while the transverse current correlation functions is not.The fifth section of the paper is devoted to the properties of a pure superconductor which depend on the lifetimes of the single-particle excitations. The effect of these lifetimes on the static electrical conductivity is determined, and it is shown that they do not destroy supercurrents although they eliminate a gap in the single-particle excitation spectrum. Their effect on the thermal conductivity is also calculated using heat current correlation functions. It is shown that a model which treats the lifetime of the single-particle excitation due to lattice interactions as constant yields results in agreement with observed thermal conductivities.