The ground state energy at unitarity

TL;DR

This paper computes the ground state energy of two-component fermions at unitarity on a lattice using advanced Monte Carlo methods, providing precise energy ratios for 10 and 14 fermions.

Contribution

It introduces an efficient auxiliary-field Monte Carlo approach with a bounded continuous field and hybrid Monte Carlo for unitarity fermions, achieving accurate energy calculations.

Findings

Ground state energy ratio for 10 fermions: 0.292(12)

Ground state energy ratio for 14 fermions: 0.329(5)

Method achieves continuum extrapolation across multiple lattice sizes.

Abstract

We consider two-component fermions on the lattice in the unitarity limit. This is an idealized limit of attractive fermions where the range of the interaction is zero and the scattering length is infinite. Using Euclidean time projection, we compute the ground state energy using four computationally different but physically identical auxiliary-field methods. The best performance is obtained using a bounded continuous auxiliary field and a non-local updating algorithm called hybrid Monte Carlo. With this method we calculate results for 10 and 14 fermions at lattice volumes 4^3, 5^3, 6^3, 7^3, 8^3 and extrapolate to the continuum limit. For 10 fermions in a periodic cube, the ground state energy is 0.292(12) times the ground state energy for non-interacting fermions. For 14 fermions the ratio is 0.329(5).