Lattice approaches to dilute Fermi gases: Legacy of broken Galilean invariance

TL;DR

This paper explores how lattice periodicity affects the properties of dilute Fermi gases, revealing universal corrections and constraints on extrapolating lattice results to continuum systems.

Contribution

It provides analytical expressions for finite-density corrections due to lattice effects across the BCS-BEC crossover, highlighting the impact of broken translational invariance.

Findings

Finite lattice spacing influences dilute Fermi gas properties even at small densities.

Universal power-law correction $n^{1/3}$ affects observables.

Results constrain lattice extrapolations to continuum Fermi gases.

Abstract

In the dilute limit, the properties of fermionic lattice models with short-range attractive interactions converge to those of a dilute Fermi gas in continuum space. We investigate this connection using mean-field and we show that the existence of a finite lattice spacing has consequences down to very small densities. In particular we show that the reduced translational invariance associated to the lattice periodicity has a pivotal role in the finite-density corrections to the universal zero-density limit. For a parabolic dispersion with a sharp cut-off, we provide an analytical expression for the leading-order corrections in the whole BCS-BEC crossover. These corrections, which stem only from the unavoidable cut-off, contribute to the leading-order corrections to the relevant observables. In a generic lattice we find a universal power-law behavior $n^{1/3}$ which leads to significant corrections already for small densities. Our results pose strong constraints on lattice extrapolations of dilute Fermi gas properties.