Entanglement signatures of quantum Hall phase transitions

TL;DR

This paper investigates quantum Hall phase transitions by analyzing entanglement properties in finite-size wavefunctions, revealing signatures of phase changes through entropy scaling and reduced density matrix characteristics.

Contribution

It introduces a numerical approach to detect quantum phase transitions in fractional quantum Hall states via entanglement measures, varying interaction potentials on spherical geometries.

Findings

Entanglement entropy scaling signals phase transitions.

Reduced density matrix features also indicate phase changes.

Signature patterns depend on interaction potential variations.

Abstract

We study quantum phase transitions involving fractional quantum Hall states, using numerical calculations of entanglements and related quantities. We tune finite-size wavefunctions on spherical geometries, by varying the interaction potential away from the Coulomb interaction. We uncover signatures of quantum phase transitions contained in the scaling behavior of the entropy of entanglement between two parts of the sphere. In addition to the entanglement entropy, we show that signatures of quantum phase transitions also appear in other aspects of the reduced density matrix of one part of the sphere.