4.6 Article

Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime

Journal

COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 374, Issue 3, Pages 2097-2150

Publisher

SPRINGER
DOI: 10.1007/s00220-019-03505-5

Keywords

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Funding

  1. Austrian Science Fund (FWF)
  2. European Research Council (ERC) under the European Union [694227]
  3. Austrian Science Fund (FWF) [P27533-N27]
  4. Swiss National Science Foundation
  5. NCCR SwissMAP

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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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