Entanglement Entropy of Quantum Hall Systems at Half Filling

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.

8 pages, 9 figures; added references