Finite-temperature second-order many-body perturbation theory revisited

TL;DR

This paper develops an algebraic derivation of finite-temperature second-order many-body perturbation theory, providing explicit formulas for energy calculations in interacting electron systems at finite temperature, and clarifies its relation to zero-temperature theory.

Contribution

It introduces an algebraic, nondiagrammatic derivation of FT-MBPT(2) with explicit energy expressions, bridging finite and zero-temperature perturbation theories.

Findings

FT-MBPT(2) reproduces ZT-MBPT(2) in the zero-temperature limit.

The approach is suitable for finite or infinite systems in thermal contact.

It clarifies the absence of the Kohn--Luttinger conundrum in this context.

Abstract

We present an algebraic, nondiagrammatic derivation of finite-temperature second-order many-body perturbation theory [FT-MBPT(2)], using techniques and concepts accessible to theoretical chemical physicists. We give explicit expressions not just for the grand potential but particularly for the mean energy of an interacting many-electron system. The framework presented is suitable for computing the energy of a finite or infinite system in contact with a heat and particle bath at finite temperature and chemical potential. FT-MBPT(2) may be applied if the system, at zero temperature, may be described using standard (i.e., zero-temperature) second-order many-body perturbation theory [ZT-MBPT(2)] for the energy. We point out that in such a situation, FT-MBPT(2) reproduces, in the zero-temperature limit, the energy computed within ZT-MBPT(2). In other words, the difficulty that has been referred to as the Kohn--Luttinger conundrum, does not occur. We comment, in this context, on a "renormalization" scheme recently proposed by Hirata and He.