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

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.

10 pages, 7 figures

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• Numerical study of the unitary Fermi gas across the superfluid transition
• Inhomogeneous BCS-BEC crossover for trapped cold atoms in optical lattices
• Improved lattice operators for non-relativistic fermions
• Interacting quantum walkers: Two-body bosonic and fermionic bound states
• Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a 2D square lattice
• Interface and bulk superconductivity in superconducting heterostructures with enhanced critical temperatures
• Thermal transitions, pseudogap behavior and BCS-BEC crossover in Fermi-Fermi mixtures
• Zero density limit extrapolation of the superfluid transition temperature in a unitary atomic Fermi gas on a lattice