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arXiv · 2310.02706

Momentum Distribution of a Fermi Gas in the Random Phase Approximation

Niels Benedikter·Sascha Lill
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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.

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Niels Benedikter, Sascha Lill. 2023-10-04. Momentum Distribution of a Fermi Gas in the Random Phase Approximation. https://arxiv.org/abs/2310.02706

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