We present a detailed study of the ground-state entanglement in disorderedfractional quantum Hall liquids. We consider electrons at various fillingfractions $f$ in the lowest Landau level, with Coulomb interactions. At$f=1/3,1/5$ and $2/5$ where an incompressible ground-state manifold exists atzero disorder, we observe a pronounced minimum in the derivative ofentanglement entropy with respect to disorder. At each filling, the position ofthis minimum is stable against increasing system size, but its magnitude growsmonotonically and appears to diverge in the thermodynamic limit. We considerthis behaviour of the entropy derivative as a compelling signal of the expecteddisorder-driven phase transition from a topological fractional quantum Hallphase to a trivial insulating phase. On the contrary, at $f=1/2$ where acompressible composite fermion sea is present at zero disorder, the entropyderivative exhibits much greater, almost chaotic, finite-size effects, withouta clear phase transition signal for system sizes within our exactdiagonalization limit. However, the dependence of entanglement entropy withsystem size changes with increasing disorder, consistent with the expectationof a phase transition from a composite fermion sea to an insulator. Finally, weconsider $f=1/7$ where compressible Wigner crystals are quite competitive atzero disorder, and analyze the level statistics of entanglement spectrum at$f=1/3$.
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机译：我们对无序分数量子霍尔液体中的基态纠缠进行了详细的研究。我们考虑了最低的朗道能级上具有库仑相互作用的各种填充分数$ f $的电子。在$ f = 1 / 3、1 / 5 $和$ 2/5 $的情况下，不可压缩的基态流形存在零杂散，我们观察到纠缠熵的无序导数最小。在每次填充时，此最小值的位置在系统尺寸增大时是稳定的，但其大小单调增长，并且在热力学极限中似乎有所不同。我们认为熵导数的这种行为是从拓扑分数量子霍尔相到平凡绝缘相的预期无序驱动相变的强制信号。相反，在$ f = 1/2 $处（零乱序处存在可压缩复合费米子海），熵导数表现出更大的，几乎是混沌的，有限大小的效果，而对于在我们精确对角化范围内的系统大小，没有清晰的相变信号。然而，纠缠熵对系统尺寸的依赖性随无序性的增加而变化，这与对从复合费米子海到绝缘子的相变的期望相一致。最后，我们考虑$ f = 1/7 $，其中可压缩的Wigner晶体具有很强的竞争性零失调，并分析了$ f = 1/3 $的纠缠谱的能级统计。
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