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

Tamás Haidekker Galambos^1,2,3 and Csaba Tőke^1,2

¹BME-MTA Exotic Quantum Phases “Lendület” Research Group, Budapest University of Technology and Economics, Institute of Physics, Budafoki út 8, H-1111 Budapest, Hungary
²Department of Theoretical Physics, Budapest University of Technology and Economics, Institute of Physics, Budafoki út 8, H-1111 Budapest, Hungary
³Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

Phys. Rev. E 97, 022140 – Published 26 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022140

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 multislice 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.

Physics Subject Headings (PhySH)

Quantum statistical mechanics

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References (38)

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

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