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Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime
Niels Benedikter1, Phan Thành Nam2, Marcello Porta3
1IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
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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