Numerical Evidence Invalidating Finite-Temperature Many-Body Perturbation Theory

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.

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• Comment on "Numerical Evidence Falsifying Finite-Temperature Many-Body Perturbation Theory"

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• Nonconvergence of the Feynman-Dyson diagrammatic perturbation expansion of propagators
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• General solution to the Kohn-Luttinger nonconvergence problem
• Finite-temperature many-body perturbation theory for vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm
• Normal ordered exponential approach to thermal properties and time-correlation functions: General theory and simple examples