Converging finite-temperature many-body perturbation theory that conserves the average number of electrons

Abstract

A finite-temperature perturbation theory for the grand canonical ensemble is introduced that expands chemical potential in a perturbation series and conserves the average number of electrons, ensuring charge neutrality of the system at each perturbation order. Two classes of (sum-over-state and reduced) analytical formulas are obtained in a straightforward, algebraic, time-independent derivation for the first-order corrections to chemical potential, grand potential, and internal energy, with the aid of several identities of the Boltzmann sums also introduced in this study. These formulas are numerically verified against benchmark data from thermal full configuration interaction. In the zero-temperature limit, the finite-temperature perturbation theory reduces analytically to and is consistent with the Møller-Plesset perturbation theory, but only for a nondegenerate ground state. For a degenerate ground state, its correct zero-temperature limit is not the Møller-Plesset perturbation theory, but the Hirschfelder-Certain degenerate perturbation theory.

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Cited by in corpus (12)

• Finite-Temperature Many-Body Perturbation Theory in the Canonical Ensemble
• Finite-temperature many-body perturbation theory in the grand canonical ensemble
• Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, grand canonical and canonical ensembles
• Numerical Evidence Invalidating Finite-Temperature Many-Body Perturbation Theory
• Nonconvergence of the Feynman-Dyson diagrammatic perturbation expansion of propagators
• Low-temperature breakdown of many-body perturbation theory for thermodynamics
• 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
• Thermal mean-field theories
• Thermal quasi-particle theory
• Complex analysis of divergent perturbation theory at finite temperature