Benedikter N, Nam PT, Porta M, Schlein B, Seiringer R. Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.
COMMUNICATIONS IN MATHEMATICAL PHYSICS 2019;
374:2097-2150. [PMID:
32675828 PMCID:
PMC7336250 DOI:
10.1007/s00220-019-03505-5]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/17/2018] [Accepted: 05/15/2019] [Indexed: 06/11/2023]
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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