Monte Carlo Evaluation of Non-Abelian Statistics

TL;DR

This paper introduces a numerical framework to study non-Abelian quasihole braiding in fractional quantum Hall systems, confirming theoretical predictions for the Moore-Read state at filling factor 1/2.

Contribution

It provides the first explicit numerical demonstration of non-Abelian statistics in the Moore-Read state, validating conformal field theory predictions.

Findings

Confirmed non-Abelian braiding statistics in Moore-Read quasiholes

Developed a general numerical framework for adiabatic braiding studies

Validated theoretical predictions with numerical evidence

Abstract

We develop a general framework to (numerically) study adiabatic braiding of quasiholes in fractional quantum Hall systems. Specifically, we investigate the Moore-Read (MR) state at $\nu=1/2$ filling factor, a known candidate for non-Abelian statistics, which appears to actually occur in nature. The non-Abelian statistics of MR quasiholes is demonstrated explicitly for the first time, confirming the results predicted by conformal field theories.