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

Thursday, 6 September, 2018

Published in: 

arXiv:1809.01902

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.

Author(s): 

Niels Benedikter
Phan Thành Nam
Marcello Porta
Benjamin Schlein
Robert Seiringer