@inbook{fcefb8c3a7e84621ae6b0acfb1630a6c,
title = "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 an ideal gas of noninteracting, identical molecules at a nonzero temperature are determined numerically as the λ-derivatives of the respective quantity calculated exactly (by thermal full configuration interaction) with a perturbation-scaled Hamiltonian, Hˆ0+λVˆ. 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 discussed in many textbooks disagree with these benchmark data. This is because the theory neglects the variation of chemical potential with λ, thereby failing to converge at the exact, full-interaction (λ = 1) limit, unless the exact chemical potential is known in advance. The renormalized finite-temperature perturbation theory (Hirata and He, 2013) (15) is also found to be incorrect.",
keywords = "Chemical potential, Grand canonical ensemble, Grand potential, Internal energy, Many-body perturbation theory, Temperature, Thermodynamics",
author = "Jha, {Punit K.} and So Hirata",
note = "Funding Information: This work was supported by the Center for Scalable, Predictive methods for Excitation and Correlated phenomena (SPEC), which is funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, as a part of the Computational Chemical Sciences Program and also by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Grant No. DE-SC0006028. We sincerely thank Dr. Alec F. White and Dr. Garnet K.-L. Chan for many corrections to earlier drafts of this paper via Ref. (19). We also thank Mr. Alexander Doran, Dr. Alexander Kunitsa, Dr. Debashis Mukherjee, Dr. Mark Pederson, Dr. Robin Santra for helpful discussions. Funding Information: This work was supported by the Center for Scalable, Predictive methods for Excitation and Correlated phenomena (SPEC), which is funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, as a part of the Computational Chemical Sciences Program and also by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Grant No. DE-SC0006028. We sincerely thank Dr. Alec F. White and Dr. Garnet K.-L. Chan for many corrections to earlier drafts of this paper via Ref. ( 19 ) . We also thank Mr. Alexander Doran, Dr. Alexander Kunitsa, Dr. Debashis Mukherjee, Dr. Mark Pederson, Dr. Robin Santra for helpful discussions. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",
year = "2019",
doi = "10.1016/bs.arcc.2019.08.002",
language = "English (US)",
isbn = "9780128171196",
series = "Annual Reports in Computational Chemistry",
publisher = "Elsevier Ltd",
pages = "3--15",
editor = "Dixon, {David A.}",
booktitle = "Annual Reports in Computational Chemistry",
}