2011
DOI: 10.1088/1367-2630/13/5/055006
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Entanglement entropy of random fractional quantum Hall systems

Abstract: The entanglement entropy of the ν = 1/3 and ν = 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, spin polarized 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 disorde… Show more

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Cited by 9 publications
(10 citation statements)
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“…An alternative approach for characterizing topological phases would be to consider the entanglement entropy across the phase transition (see e.g. [49][50][51])…”
Section: Strongly Attractive Regimementioning
confidence: 99%
“…An alternative approach for characterizing topological phases would be to consider the entanglement entropy across the phase transition (see e.g. [49][50][51])…”
Section: Strongly Attractive Regimementioning
confidence: 99%
“…Unfortunately, due to the exponentially large Hilbert space of the underlying many-body system as well as the breaking of spatial symmetry, it is challenging to study in the microscopic level how disorder affects FQH phases. In the past decades, only a few numerical studies tackle this problem for fermionic FQH systems [24][25][26][27][28][29]. By tracking the evolution of the ground-state energy gap, Hall conductance, and entanglement entropy as a function of disorder strength, disorder-driven transitions from Abelian and non-Abelian FQH phases to trivial phases were identified in microscopic models.…”
Section: Introductionmentioning
confidence: 99%
“…Using a model of short range disorder introduced in 6,7 , the entanglement entropy for the 1 3 and 5 2 states was calculated as a function of the disorder strength 8 . The entanglement entropy for the purposes of the present paper (and 8 ) is the Von Neumann entropy of the reduced density matrix when the whole system is partitioned into two parts; call them the subsystem and the environment.…”
Section: Introductionmentioning
confidence: 99%
“…The entanglement entropy has good formal properties 9 , it obeys strong subadditivity, however, it is difficult to calculate, in comparison to other Renyi entropies 10 and it is very difficult to measure directly as it involves the reduced density matrix of a many body system. Direct diagonalization results 8 experiment, a parameter describing layer thickness must be introduced. One is faced with the apparently paradoxical situation where layer thickness is unnecessary to describe short range disorder in the 5 2 state, while layer thickness is needed for 1 3 filling.…”
Section: Introductionmentioning
confidence: 99%