An optimal lower bound for the low density Fermi gas in three dimensions

TL;DR

This paper establishes an optimal second order lower bound for the ground state energy density of a dilute three-dimensional Fermi gas, matching the conjectured correction term by Huang-Yang, thus advancing understanding of quantum many-body systems.

Contribution

It provides the first rigorous proof of an optimal lower bound for the energy of the dilute Fermi gas in three dimensions, confirming long-standing conjectures.

Findings

Proved a second order lower bound matching the Huang-Yang correction

Validated the conjectured correction term for the Fermi gas energy

Enhanced theoretical understanding of dilute quantum gases

Abstract

We consider the dilute Fermi gas in three dimensions interacting through a positive, radially symmetric, compactly supported and integrable potential in the thermodynamic limit. We establish a second order lower bound for the ground state energy density with an error term which is optimal in the sense that it matches the order of the next correction term conjectured by Huang-Yang in 1957.