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Entanglement Entropy of Quantum Hall Systems at Half Filling

The entanglement entropy of $ν=1/2$ and $ν=9/2$ 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 $ν=1/2$ the entanglement entropy is a smooth monotonic function of disorder strength. For $ν=9/2$ the entanglement entropy is non monotonic suggestive of a solid-liquid phase transition. As a model of the transition at $ν=1/2$ 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.