Entanglement Entropy of Quantum Hall Systems at Half Filling

TL;DR

This paper investigates how entanglement entropy behaves in quantum Hall systems at half filling with disorder, revealing different behaviors at filling factors 1/2 and 9/2, and suggesting phase transition signatures.

Contribution

It provides numerical calculations of entanglement entropy in disordered quantum Hall states, highlighting non-monotonic behavior and scaling laws indicative of phase transitions.

Findings

Entanglement entropy at ν=1/2 is a smooth, monotonic function of disorder.

At ν=9/2, entanglement entropy shows non-monotonic behavior, suggesting a phase transition.

In a 2D free fermion model, entanglement entropy scales linearly with system size L.

Abstract

The entanglement entropy of $\nu=1/2$ and $\nu=9/2$ quantum Hall states in the presence of short range disorder has been calculated by direct diagonalization. Spin polarized electrons are confined to a single Landau level and interact with long range Coulomb interaction. For $\nu=1/2$ the entanglement entropy is a smooth monotonic function of disorder strength. For $\nu=9/2$ the entanglement entropy is non monotonic suggestive of a solid-liquid phase transition. As a model of the transition at $\nu=1/2$ free fermions with disorder in 2 dimensions were studied. Numerical evidence suggests the entanglement entropy scales as $L$ rather than the $L \ln{L}$ as in the disorder free case.