Momentum Distribution of a Fermi Gas in the Random Phase Approximation

TL;DR

This paper demonstrates that the random phase approximation accurately captures the Fermi surface and momentum distribution in an interacting Fermi gas, confirming the presence of a Fermi liquid phase in the mean-field limit.

Contribution

It proves that the RPA can identify a non-trivial Fermi liquid phase and shows the universality of the Fermi momentum regardless of interaction potential.

Findings

The momentum distribution has a jump discontinuity indicating a Fermi surface.

The Fermi momentum is independent of the interaction potential.

The RPA is sufficiently precise for identifying Fermi liquid behavior.

Abstract

We consider a system of interacting fermions on the three-dimensional torus in a mean-field scaling limit. Our objective is computing the occupation number of the Fourier modes in a trial state obtained through the random phase approximation (in its collective bosonization formulation) for the ground state. We prove that the trial state's momentum distribution has a jump discontinuity, i.e., a well-defined Fermi surface. Moreover the Fermi momentum does not depend on the interaction potential (it is universal). Our result shows that the random phase approximation in the mean-field scaling limit is in principle sufficiently precise to identify a non-trivial Fermi liquid phase.