Non-Abelian fusion and braiding in many-body parton states

TL;DR

This paper constructs quasihole bases for non-Abelian fractional quantum Hall states using parton wave functions, and numerically computes braiding matrices to diagnose non-Abelian properties in large systems.

Contribution

It introduces a method to build quasihole bases for non-Abelian FQH states with parton wave functions and computes braiding matrices for large systems.

Findings

Quasihole bases match conformal field theory predictions.

Braiding matrices confirm non-Abelian statistics.

Framework applicable to various candidate FQH states.

Abstract

Fractional quantum Hall (FQH) states host fractionally charged anyons with exotic exchange statistics. Of particular interest are FQH phases supporting non-Abelian anyons, which can encode topologically protected quantum information. In this work, we construct quasihole bases for a broad family of non-Abelian FQH states using parton wave functions, which reproduces the fusion-space dimensionality expected from their underlying conformal field theory, consistent with level-rank duality across the parton family. As an application, we numerically compute braiding matrices for representative parton states for large systems, providing a general framework for diagnosing non-Abelian characteristics in candidate FQH states.