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arXiv:2310.02706 · Journal of Mathematical Physics

Momentum distribution of a Fermi gas in the random phase approximation

Niels Benedikter, Sascha Lill

Published Aug 1, 2025• 1 citation
arXivHTMLPDF

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.

DOI
10.1063/5.0268726

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Abstract We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We consider a system of N fermions on a torus, interacting via a two-body repulsive potential proportional to N−13N^{-\frac {1}{3}}N−31​ . In the limit $N\rightarrow \infty $ , we derive the exact leading order of the correlation energy and the bosonic elementary excitations of the system, which are consistent with the prediction of the random phase approximation in the physics literature.
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