Thermal quasi-particle theory

TL;DR

This paper extends thermal Hartree-Fock theory to include electron correlation effects using second-order many-body perturbation theory, providing a more accurate finite-temperature description of electronic systems while maintaining thermodynamic consistency.

Contribution

It introduces a generalized thermal quasi-particle theory incorporating electron correlation within a quasi-independent-particle framework, based on second-order MBPT.

Findings

The theory obeys all fundamental thermodynamic relations.

It approaches finite-temperature MBPT at low temperatures.

It may outperform standard MBPT at intermediate temperatures by including additional correlation effects.

Abstract

The widely used thermal Hartree-Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasi-particle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi-Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi-Dirac or thermal HF theory. The theory thus constitutes a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green's function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperature, the theory approaches finite-temperature MBPT of the same order, but it may outperform the latter at intermediate temperature by including additional electron-correlation effects through orbital energies. A physical meaning of these thermal orbital energies is proposed (encompassing that of thermal HF orbital energies, which has been elusive) as a finite-temperature version of Janak's theorem.