Correlation Energy of a Weakly Interacting Fermi Gas

Niels Benedikter, Phan Thành Nam, Marcello Porta, Benjamin Schlein, Robert Seiringer

Published 2020-05-18Version 1

We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.