Numerical Evidence Invalidating Finite-Temperature Many-Body Perturbation Theory

TL;DR

This paper provides numerical evidence that finite-temperature many-body perturbation theory fails to accurately predict thermodynamic properties of noninteracting molecules, due to neglecting chemical potential variations, challenging its validity.

Contribution

The study introduces benchmark data for finite-temperature perturbation corrections and demonstrates the failure of existing theories to match these benchmarks.

Findings

First- and second-order corrections disagree with benchmarks.

Neglect of chemical potential variation causes divergence at full interaction.

Renormalized perturbation theory also found to be incorrect.

Abstract

Low-order perturbation corrections to the electronic grand potential, internal energy, chemical potential, and entropy of a gas of noninteracting, identical molecules at a nonzero temperature are determined numerically as the $\lambda$-derivatives of the respective quantity calculated exactly (by thermal full configuration interaction) with a perturbation-scaled Hamiltonian, $\hat{H}_0 + \lambda\hat{V}$. The data thus obtained from the core definition of any perturbation theory serve as a benchmark against which analytical formulas can be validated. The first- and second-order corrections from finite-temperature many-body perturbation theory disagree with these benchmark data. This is because the theory neglects the variation of chemical potential with $\lambda$, thereby failing to converge at the exact, full-interaction ($\lambda=1$) limit, unless the exact chemical potential is known in advance. The renormalized finite-temperature perturbation theory [S. Hirata and X. He, J. Chem. Phys., 138, 204112 (2013)] is also found to be incorrect.