Transdimensional equivalence of universal constants for Fermi gases at unitarity

TL;DR

This paper uses lattice Monte Carlo methods to calculate the Bertsch parameter for a one-dimensional four-component Fermi gas, revealing a possible universal connection to three-dimensional systems and demonstrating consistency with analytical results.

Contribution

It provides the first nonperturbative lattice calculations of the Bertsch parameter in 1D and explores its universality with 3D Fermi gases at unitarity.

Findings

Bertsch parameter in 1D is ~0.370, matching 3D estimates within 1%

Continuum energies for 4 and 5 fermions agree with analytical results within 1%

Restoration of Virial theorem in the continuum limit is demonstrated

Abstract

I present lattice Monte Carlo calculations for a universal four-component Fermi gas confined to a finite box and to a harmonic trap in one spatial dimension. I obtain the values xi_1d = 0.370(4) and xi_1d = 0.372(1), respectively, for the Bertsch parameter, a nonperturbative universal constant defined as the (square of the) energy of the untrapped (trapped) system measured in units of the free gas energy. The Bertsch parameter for the one-dimensional system is consistent to within ~1% uncertainties with the most recent numerical and experimental estimates of the analogous Bertsch parameter for a three-dimensional spin-1/2 Fermi gas at unitarity. The finding suggests the intriguing possibility that there exists a universality between two conformal theories in different dimensions. To lend support to this study, I also compute continuum extrapolated ground state energies for four and five fermions confined to a harmonic trap and demonstrate the restoration of a Virial theorem in the continuum limit. The continuum few-body energies obtained are consistent with exact analytical calculations to within ~1.0% and ~0.25% statistical uncertainties, respectively.