A complex Langevin approach to ultracold fermions

TL;DR

This paper applies the Complex Langevin method to study one-dimensional mass-imbalanced Fermi gases, overcoming the sign problem and achieving results consistent with other approaches, with potential for extension to more complex systems.

Contribution

It introduces the Complex Langevin approach for simulating mass-imbalanced Fermi gases, enabling studies beyond current limitations and applicable to higher dimensions.

Findings

Achieved agreement with existing methods in a range of parameters

Demonstrated the method's effectiveness for both attractive and repulsive interactions

Showed potential for extension to finite spin polarization and higher dimensions

Abstract

The theoretical treatment of Fermi systems consisting of particles with unequal masses is challenging. Even in one spatial dimension analytic solutions are limited to special configurations and numerical progress with Monte Carlo simulations is hindered by the sign-problem. To circumvent this issue, we exploit the Complex Langevin approach and study one-dimensional mass-imbalanced two-component Fermi gases with attractive and repulsive interactions. We find perfect agreement with results obtained by other methods in a range of parameter space. Promisingly, our approach is not limited to the specific model presented here and can easily be extended to finite spin polarization and, most notably, can also be applied in higher dimensions.