Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

TL;DR

This paper introduces a new lattice Monte Carlo method for studying large, strongly interacting fermion systems in a harmonic trap, achieving high precision results with reduced errors and computational efficiency.

Contribution

The authors develop a highly improved lattice Monte Carlo approach that minimizes discretization and finite volume errors, enabling precise calculations of large fermion systems without importance sampling.

Findings

Accurately reproduces known energies for small fermion numbers

Determines ground state energies for up to 70 fermions in a trap

Achieves high precision with modest computational resources

Abstract

We present a new lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions, and apply it to a dilute gas of unitary fermions confined to a harmonic trap. Our lattice action is highly improved, with sources of discretization and finite volume errors systematically removed; we are able to demonstrate the expected volume scaling of energy levels of two and three untrapped fermions, and to reproduce the high precision calculations published previously for the ground state energies for N = 3 unitary fermions in a box (to within our 0.3% uncertainty), and for N = 3, . . ., 6 unitary fermions in a harmonic trap (to within our ~ 1% uncertainty). We use this action to determine the ground state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as 64^3 x 72; our approach avoids the use of importance sampling or calculation of a fermion determinant and employs a novel statistical method for estimating observables, allowing us to generate ensembles as large as 10^8 while requiring only relatively modest computational resources.