Hybrid Monte Carlo for fractional quantum Hall states

We develop a hybrid Monte Carlo (HMC) method to efficiently compute the physical observables from the samplings of the Laughlin and the Moore-Read (MR) wave functions of fractional quantum Hall (FQH) systems. With the advancements in methodology, including global updates and double stereographic projection on spherical geometry, our HMC simulation is significantly faster than the widely used Metropolis Monte Carlo scheme. As a result, we can readily simulate systems with electron numbersN>1000on both disk and sphere geometries. We apply this method to investigate the topological shift obtained from the edge dipole moment, computed from the wave function density on the disk. We also numerically computed the non-Abelian braiding matrices for different braiding schemes of the MR 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 FQH states in an ideal Chern band setting or under quantum decoherence.