Entanglement Entropy of Random Fractional Quantum Hall Systems

TL;DR

This study calculates the entanglement entropy in fractional quantum Hall systems with disorder, revealing a quantum phase transition at certain disorder levels, and discusses methods for analyzing larger systems.

Contribution

It provides the first detailed analysis of entanglement entropy in disordered fractional quantum Hall states using exact diagonalization and explores the potential of DMRG for larger systems.

Findings

Topological entanglement entropy aligns with theory at weak disorder.

Detected a quantum phase transition at specific disorder strength for ν=5/2.

Disorder induces fluctuations in entanglement entropy indicating phase changes.

Abstract

The entanglement entropy of the $\nu = 1/3$ and $\nu = 5/2$ quantum Hall states in the presence of short range random disorder has been calculated by direct diagonalization. A microscopic model of electron-electron interaction is used, electrons are confined to a single Landau level and interact with long range Coulomb interaction. For very weak disorder, the values of the topological entanglement entropy are roughly consistent with expected theoretical results. By considering a broader range of disorder strengths, the fluctuation in the entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a clear signature of a transition as a function of the disorder strength for the $\nu = 5/2$ state. Prospects for using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed.