Finite-density corrections to the Unitary Fermi gas: A lattice perspective from Dynamical Mean-Field Theory

TL;DR

This study uses Dynamical Mean-Field Theory to analyze how finite-density effects influence the properties of the unitary Fermi gas on various lattice models, aiming to understand the approach to the universal dilute regime.

Contribution

It demonstrates how different lattice geometries affect finite-density corrections and compares DMFT results with Monte Carlo simulations at low densities.

Findings

Finite-density effects vary significantly with lattice type.

The lattice gas model minimizes finite-density effects.

DMFT results agree with Monte Carlo simulations at low densities.

Abstract

We investigate the approach to the universal regime of the dilute unitary Fermi gas as the density is reduced to zero in a lattice model. To this end we study the chemical potential, superfluid order parameter and internal energy of the attractive Hubbard model in three different lattices with densities of states (DOS) which share the same low-energy behavior of fermions in three-dimensional free space: a cubic lattice, a "Bethe lattice" with a semicircular DOS, and a "lattice gas" with parabolic dispersion and a sharp energy cut-off that ensures the normalization of the DOS. The model is solved using Dynamical Mean-Field Theory, that treats directly the thermodynamic limit and arbitrarily low densities, eliminating finite-size effects. At densities of the order of one fermion per site the lattice and its specific form dominate the results. The evolution to the low-density limit is smooth and it does not allow to define an unambiguous low-density regime. Such finite-density effects are significantly reduced using the lattice gas, and they are maximal for the three-dimensional cubic lattice. Even though dynamical mean-field theory is bound to reduce to the more standard static mean field in the limit of zero density due to the local nature of the self-energy and of the vertex functions, it compares well with accurate Monte Carlo simulations down to the lowest densities accessible to the latter.