Benedikter, Niels; Phan Thimh, Nam; Porta, Marcello; Schlein, Benjamin; Seiringer, Robert
(2020):
Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the MeanField Regime.
In: Communications in Mathematical Physics, Vol. 374, No. 3: pp. 20972150

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Abstract
While HartreeFock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to manybody correlations. In this paper we start from the HartreeFock state given by plane waves and introduce collective particlehole 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 GellMannBruecknertype upper bound to the ground state energy. Our result justifies the randomphase approximation in the meanfield scaling regime, for repulsive, regular interaction potentials.