Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential

Niels Benedikter, Marcello Porta, Benjamin Schlein, Robert Seiringer

Published 2021-06-24Version 1

Recently the leading order of the correlation energy of a Fermi gas in a mean-field scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only $|.| \hat{V} \in \ell^1 (\mathbb{Z}^3)$. Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy.