# Path-integral Monte Carlo simulation of time-reversal noninvariant bulk systems with a case study of rotating Yukawa gases

## TL;DR

This paper develops a path-integral Monte Carlo method for simulating bulk systems without time-reversal symmetry, applying it to study vortex melting in rotating Yukawa gases relevant to ultracold atomic systems.

## Contribution

It introduces a phase-fixed Monte Carlo approach with closed-form density matrix expressions and modified sampling techniques for non-time-reversal-invariant systems.

## Key findings

- Successfully simulated vortex melting in rotating Yukawa gases.
- Provided analytical expressions for thermal density matrices on a torus.
- Demonstrated applicability to ultracold Fermi-Fermi mixtures under rotation.

## Abstract

We elaborate on the methodology to simulate bulk systems in the absence of time-reversal symmetry by the phase-fixed path-integral Monte Carlo method under (possibly twisted) periodic boundary conditions. Such systems include two-dimensional electrons in the quantum Hall regime and rotating ultracold Bose and Fermi gases; time-reversal symmetry is broken by an external magnetic field and the Coriolis force, respectively. We provide closed-form expressions in terms of Jacobi elliptic functions for the thermal density matrix (or the Euclidean propagator) of a single particle on a flat torus under very general conditions. We then modify the multi-slice sampling method in order to sample paths by the magnitude of the complex-valued thermal density matrix. Finally, we demonstrate that these inventions let us study the vortex melting process of a two-dimensional Yukawa gas in terms of the de Boer interaction strength parameter, temperature, and rotation (Coriolis force). The bosonic case is relevant to ultracold Fermi-Fermi mixtures of widely different masses under rotation.