Low-temperature breakdown of many-body perturbation theory for thermodynamics

Hirata, So

doi:10.1103/physreva.103.012223

Low-temperature breakdown of many-body perturbation theory for thermodynamics

Journal Article · Tue Jan 26 00:00:00 EST 2021 · Physical Review A

DOI:https://doi.org/10.1103/physreva.103.012223· OSTI ID:1762416

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Univ. of Illinois at Urbana-Champaign, IL (United States); University of Illinois at Urbana-Champaign

It is shown analytically and numerically that the finite-temperature many-body perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy ordering or degree of degeneracy for the ground state changes with the perturbation strength. When the degeneracy of the reference state is partially or fully lifted at the first-order Hirschfelder-Certain degenerate perturbation theory, the grand potential and internal energy diverge as T → 0. Contrary to earlier suggestions of renormalizability by the chemical potential μ, this nonconvergence, first suspected by W. Kohn and J. M. Luttinger, is caused by the nonanalytic nature of the Boltzmann factor e^–E/k_eT at T = 0, also plaguing the canonical ensemble, which does not involve chemical potential. The finding reveals a fundamental flaw in perturbation theory, which is deeply rooted in the mathematical limitation of power-series expansions and is unlikely to be removed within its framework.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0006028

OSTI ID:: 1762416

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 103; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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