Density profiles and correlations of harmonically trapped ultracold fermions via complex Langevin

TL;DR

This paper investigates the use of complex Langevin stochastic quantisation to address the sign problem in lattice simulations of ultracold Fermi gases with contact interactions, providing results on density profiles and correlations in one dimension.

Contribution

It demonstrates the applicability of complex Langevin methods to non-relativistic Fermi gases with repulsive interactions, overcoming the sign problem in lattice simulations.

Findings

Results converge with adaptive step size and Gaussian regulator

Density profiles of trapped fermions are successfully computed

Correlations in the system are analyzed

Abstract

Standard lattice formulations of non-relativistic Fermi gases with two spin components suffer from a sign problem in the cases of repulsive contact interactions and attractive contact interactions with spin imbalance. We discuss the nature of this sign problem and the applicability of stochastic quantisation with complex Langevin evolution in both cases. For repulsive interactions, we find that the results converge, using adaptive step size scaling and a Gaussian regulator to modify the lattice action. We present results on density profiles and correlations of a harmonically trapped system in one spatial dimension.