Evolution of quantum entanglement with disorder in fractional quantum Hall liquids

Abstract

We present a detailed study of the ground-state entanglement in disordered fractional quantum Hall liquids. We consider electrons at various filling fractions $f$ in the lowest Landau level, with Coulomb interactions. At $f=1/3,1/5$ and $2/5$ where an incompressible ground-state manifold exists at zero disorder, we observe a pronounced minimum in the derivative of entanglement entropy with respect to disorder. At each filling, the position of this minimum is stable against increasing system size, but its magnitude grows monotonically and appears to diverge in the thermodynamic limit. We consider this behaviour of the entropy derivative as a compelling signal of the expected disorder-driven phase transition from a topological fractional quantum Hall phase to a trivial insulating phase. On the contrary, at $f=1/2$ where a compressible composite fermion sea is present at zero disorder, the entropy derivative exhibits much greater, almost chaotic, finite-size effects, without a clear phase transition signal for system sizes within our exact diagonalization limit. However, the dependence of entanglement entropy with system size changes with increasing disorder, consistent with the expectation of a phase transition from a composite fermion sea to an insulator. Finally, we consider $f=1/7$ where compressible Wigner crystals are quite competitive at zero disorder, and analyze the level statistics of entanglement spectrum at $f=1/3$.

arXiv comment12 pages, 10 figures, published version

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• Disorder broadening of even denominator fractional quantum Hall states in the presence of a short-range alloy potential
• Topology and many-body localization
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• Scaling of entanglement entropy at quantum critical points in random spin chains
• Short and Long Ranged Impurities in Fractional Quantum Hall Systems
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures