TY - JOUR

T1 - Evolution of quantum entanglement with disorder in fractional quantum Hall liquids

AU - Liu, Zhao

AU - Bhatt, R. N.

N1 - Funding Information:
We thank S. Geraedts, Z. Papic, and K. Yang for useful discussions, and an anonymous referee for useful comments. This work was supported by the Department of Energy, Office of Basic Energy Sciences through Grant No. DE-SC0002140. Z.L. was also supported by an Alexander von Humboldt Research Fellowship for Postdoctoral Researchers. R.N.B. thanks the Aspen Center for Physics for hospitality while this paper was being completed.
Publisher Copyright:
© 2017 American Physical Society.

PY - 2017/9/7

Y1 - 2017/9/7

N2 - 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 behavior of the entropy derivative as a compelling signal of the expected disorder-driven phase transition from a topological fractional quantum Hall phase to an 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.

AB - 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 behavior of the entropy derivative as a compelling signal of the expected disorder-driven phase transition from a topological fractional quantum Hall phase to an 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.

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U2 - 10.1103/PhysRevB.96.115111

DO - 10.1103/PhysRevB.96.115111

M3 - Article

AN - SCOPUS:85030179396

SN - 2469-9950

VL - 96

JO - Physical Review B

JF - Physical Review B

IS - 11

M1 - 115111

ER -