Universal properties of the FQH state from the topological entanglement entropy and disorder effects

TL;DR

This paper investigates the topological entanglement entropy in fractional quantum Hall states, examining how non-Abelian quasiholes and disorder influence topological order and localization phenomena.

Contribution

It provides new insights into the stability of topological entanglement entropy under disorder and the role of non-Abelian quasiholes in FQH states.

Findings

TEE remains stable before spectral gap closes

Disorder induces many-body localization transition

Non-Abelian quasiholes affect quantum dimension measurements

Abstract

The topological entanglement entropy (TEE) is a robust measurement of the quantum many-body state with topological order. In fractional quantum Hall (FQH) state, it has a connection to the quantum dimension of the state itself and its quasihole excitations from the conformal field theory (CFT) description. We study the entanglement entropy (EE) in the Moore-Read (MR) and Read-Rezayi (RR) FQH states. The non-Abelian quasi- hole excitation induces an extra correction of the TEE which is related to its quantum dimension. With considering the effects of the disorder, the ground state TEE is stable before the spectral gap closing and the level statistics seems to have significant change with a stronger disorder, which indicates a many-body localization (MBL) transition.