Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations

TL;DR

This paper introduces a novel method using torus geometry to accurately analyze the entanglement entropy scaling in fractional quantum Hall states, enhancing topological entropy extraction and numerical difficulty assessment.

Contribution

The authors develop a new approach leveraging geometric deformations of the torus to improve entanglement entropy analysis in fractional quantum Hall states.

Findings

Accurate extraction of topological entanglement entropy.

Enhanced precision over spherical or disc geometries.

Provides insights into numerical challenges of FQH states.

Abstract

We present a new approach to obtaining the scaling behavior of the entanglement entropy in fractional quantum Hall states from finite-size wavefunctions. By employing the torus geometry and the fact that the torus aspect ratio can be readily varied, we can extract the entanglement entropy of a spatial block as a continuous function of the block boundary. This approach allows us to extract the topological entanglement entropy with an accuracy superior to what is possible on the spherical or disc geometry, where no natural continuously variable parameter is available. Other than the topological information, the study of entanglement scaling is also useful as an indicator of the difficulty posed by fractional quantum Hall states for various numerical techniques.