Braiding non-Abelian quasiholes in fractional quantum Hall states

TL;DR

This paper uses matrix product state techniques to analyze non-Abelian quasiholes in fractional quantum Hall states, providing microscopic verification of their properties and exploring their braiding statistics.

Contribution

It offers the first microscopic verification of Fibonacci quasiholes in the $ ext{Z}_3$ Read-Rezayi state and examines quasihole properties across different fractional quantum Hall states.

Findings

Estimated quasihole radii for Moore-Read and Z3 Read-Rezayi states

Determined correlation lengths for braiding statistics convergence

Provided evidence for the failure of plasma screening in Gaffnian wave function

Abstract

Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the $\mathbb{Z}_3$ Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the $\mathbb{Z}_3$ Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the non-unitary Gaffnian wave function.