Hybrid Monte Carlo for Fractional Quantum Hall States

TL;DR

This paper introduces a hybrid Monte Carlo method that significantly accelerates the simulation of fractional quantum Hall states, enabling analysis of larger systems and more accurate topological properties.

Contribution

The paper presents a novel hybrid Monte Carlo algorithm with global updates and stereographic projection, improving efficiency over traditional methods for FQH state simulations.

Findings

Simulated systems with over 1000 electrons on disk and sphere geometries.

Achieved higher quality results for braiding matrices of Moore-Read quasiholes.

Provided insights into topological shifts and potential applications in Chern band studies.

Abstract

We develop a hybrid Monte Carlo method to efficiently compute the physical observables from the samplings of the Laughlin and the Moore-Read wave functions of fractional quantum Hall (FQH) systems. With the advancements in methodology, including global updates and double stereographic projection on spherical geometry, our hybrid Monte Carlo simulation is significantly faster than the widely used Metropolis Monte Carlo scheme. As a result, we can readily simulate systems with electron numbers $N > 1000$ on both disk and sphere geometries. We apply this method to investigating the topological shift obtained from the edge dipole moment, computed from the density of the wave function on the disk. We also numerically computed the non-Abelian braiding matrices for different braiding schemes of the Moore-Read quasiholes on the sphere. Results with much better quality compared with previous works have been achieved. With the thermodynamic limit results obtained at ease, we also discuss the future usage of our method to clarify the questions on the instability of fractional quantum Hall states in an ideal Chern band setting or under quantum decoherence.