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Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime


Benedikter, Niels; Nam, Phan Thành; Porta, Marcello; Schlein, Benjamin; Seiringer, Robert (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics, 374(3):2097-2150.

Abstract

While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.

Abstract

While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Mathematical Physics, Statistical and Nonlinear Physics
Language:English
Date:1 March 2020
Deposited On:16 Dec 2019 09:36
Last Modified:14 Mar 2020 02:03
Publisher:Springer
ISSN:0010-3616
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s00220-019-03505-5
Project Information:
  • : FunderH2020
  • : Grant ID694227
  • : Project TitleAQUAMS - Analysis of quantum many-body systems

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