Lattice Monte Carlo calculations for unitary fermions in a finite box

TL;DR

This paper uses lattice Monte Carlo simulations to accurately determine the energy of a unitary Fermi gas and analyze its spectrum, improving computational methods and validating results against benchmarks.

Contribution

It introduces a highly improved lattice action for nonrelativistic fermions and provides precise calculations of the Bertsch parameter and fermion spectrum, with validation against other studies.

Findings

Bertsch parameter estimated as 0.366^{+0.016}_{-0.011}

Spectrum of up to four fermions computed and validated

Improved lattice action reduces errors from higher partial waves

Abstract

We perform lattice Monte Carlo simulations for up to 66 unitary fermions in a finite box using a highly improved lattice action for nonrelativistic spin 1/2 fermions. We obtain a value of $0.366^{+0.016}_{-0.011}$ for the Bertsch parameter, defined as the energy of the unitary Fermi gas measured in units of the free gas energy in the thermodynamic limit. In addition, for up to four unitary fermions, we compute the spectrum of the lattice theory by exact diagonalization of the transfer matrix projected onto irreducible representations of the octahedral group for small to moderate size lattices, providing an independent check of our few-body simulation results. We compare our exact numerical and simulation results for the spectrum to benchmark studies of other research groups, as well as perform an extended analysis of our lattice action improvement scheme, including an analysis of the errors associated with higher partial waves and finite temporal discretization.