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Benedikter, Niels; Phan Thimh, Nam; Porta, Marcello; Schlein, Benjamin and Seiringer, Robert (2020): Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime. In: Communications in Mathematical Physics, Vol. 374, No. 3: pp. 2097-2150

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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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