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

摘要

We present an algebraic, nondiagrammatic derivation of finite-temperaturesecond-order many-body perturbation theory [FT-MBPT(2)], using techniques andconcepts accessible to theoretical chemical physicists. We give explicitexpressions not just for the grand potential but particularly for the meanenergy of an interacting many-electron system. The framework presented issuitable for computing the energy of a finite or infinite system in contactwith 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 describedusing standard (i.e., zero-temperature) second-order many-body perturbationtheory [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 computedwithin ZT-MBPT(2). In other words, the difficulty that has been referred to asthe Kohn--Luttinger conundrum, does not occur. We comment, in this context, ona "renormalization" scheme recently proposed by Hirata and He.