Fermi gases with imaginary mass imbalance and the sign problem in Monte Carlo calculations

TL;DR

This paper proposes a novel Monte Carlo approach using imaginary mass imbalance to overcome the sign problem in simulating strongly coupled Fermi gases, enabling exploration of their phase diagram.

Contribution

It introduces a method to study mass-imbalanced Fermi gases with Monte Carlo simulations by circumventing the sign problem through imaginary mass imbalance.

Findings

Potential to detect critical points in the phase diagram.

Applicability to zero-temperature limit calculations.

Extension of analytic continuation techniques to mass imbalance.

Abstract

Fermi gases in strongly coupled regimes, such as the unitary limit, are inherently challenging for many-body methods. Although much progress has been made with purely analytic methods, quantitative results require ab initio numerical approaches, such as Monte Carlo (MC) calculations. However, mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations due to the infamous sign problem. It was recently pointed out that the sign problem, for finite spin imbalance, can be circumvented by resorting to imaginary polarizations and analytic continuation. Large parts of the phase diagram spanned by temperature and polarization then become accessible to MC calculations. We propose to apply a similar strategy to the mass-imbalanced case, which opens up the possibility to study the associated phase diagram with MC calculations. In particular, our analysis suggests that a detection of a (tri-)critical point in this phase diagram is possible. We also discuss calculations in the zero-temperature limit with our approach.