Many-Anyon Braiding in Non-Abelian Fractional Quantum Hall Effect with Hybrid Monte Carlo Simulation

Abstract

We employ the hybrid Monte Carlo method to efficiently compute the many-anyon non-Abelian braiding matrices associated with different braiding schemes of the Moore-Read quasiholes. A novel proposal in this work is that anyon braiding schemes based on a global rotation are robust against finite-size effects, as demonstrated by benchmarking their errors in the braiding matrix against those of a simple two-anyon exchange. Moreover, we investigate how electron-electron interactions and local electrostatic trapping potentials influence the energetic preference of different fusion channels. Their effect on the non-Abelian braiding matrices has been verified, a surprising phenomenon that demonstrates long-range entanglement of non-Abelian states. Our results are relevant to the experimental realization of non-Abelian physics in fractional quantum Hall and other analogous systems, including the fast-growing field of fractional quantum anomalous Hall states in moir\'e materials.