The critical value of the mobility for which the ν = 5/2 quantum Hall effect is destroyed by short range disorder is determined from an earlier calculation of the entanglement entropy. The value μ = 2.0 ×106 cm 2/ Vs agrees well with experiment. This agreement is particularly significant in that there are no adjustable parameters. Entanglement entropy versus disorder strength for ν = 1/2, ν = 9/2 and ν = 7/3 is calculated. For ν = 1/2 there is no evidence for a transition for the disorder strengths considered; for ν = 9/2 there appears to be a stripe-liquid transition. For ν = 7/3 there again appears to be a transition at similar value of the disorder strength as the ν = 5/2 transition but there are stronger finite size effects.The critical value of the mobility for which the ν = 5/2 quantum Hall effect is destroyed by short range disorder is determined from an earlier calculation of the entanglement entropy. The value μ = 2.0 ×106 cm 2/ Vs agrees well with experiment. This agreement is particularly significant in that there are no adjustable parameters. Entanglement entropy versus disorder strength for ν = 1/2, ν = 9/2 and ν = 7/3 is calculated. For ν = 1/2 there is no evidence for a transition for the disorder strengths considered; for ν = 9/2 there appears to be a stripe-liquid transition. For ν = 7/3 there again appears to be a transition at similar value of the disorder strength as the ν = 5/2 transition but there are stronger finite size effects.

International Journal of Modern Physics BFeb 5, 20155 citations

Entanglement Entropy of Quantum Hall Systems at Half Filling

Curtis Balusek, Barry Friedman, Gregory Levine +1 more

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.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.

arXiv:1205.5225May 23, 20120 citations

Topological Entanglement Entropy of Realistic Quantum Hall States

Barry Friedman, Greg Levine

Bulletin of the American Physical SocietyMar 19, 20090 citations

Entanglement entropy in extended quantum systems

John Cardy

arXiv:0708.2978The European Physical Journal BMar 11, 200832 citations

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.