Abelian topological order of $\nu=2/5$ and $3/7$ fractional quantum Hall states in lattice models

TL;DR

This study investigates the Abelian topological order of fractional quantum Hall states at filling factors 2/5 and 3/7 in lattice models, using entanglement entropy and advanced simulations to confirm their properties.

Contribution

The paper introduces an efficient algorithm to analyze entanglement entropy in lattice models, confirming Abelian topological order of specific fractional quantum Hall states.

Findings

Both states exhibit Abelian topological order with two-body interactions.

The method accounts for numerical and statistical errors in entanglement calculations.

Sensitivity of topological order to interaction range and strength is discussed.

Abstract

Determining the statistics of elementary excitations supported by fractional quantum Hall states is crucial to understanding their properties and potential applications. In this paper, we use the topological entanglement entropy as an indicator of Abelian statistics to investigate the single-component $\nu=2/5$ and $3/7$ states for the Hofstadter model in the band mixing regime. We perform many-body simulations using the infinite cylinder density matrix renormalization group and present an efficient algorithm to construct the area law of entanglement, which accounts for both numerical and statistical errors. Using this algorithm, we show that the $\nu=2/5$ and $3/7$ states exhibit Abelian topological order in the case of two-body nearest-neighbor interactions. Moreover, we discuss the sensitivity of the proposed method and fractional quantum Hall states with respect to interaction range and strength.