Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
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随机二次哈密顿量中的本征态纠缠熵
DOI：
10.1103/physrevlett.125.180604
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发表时间：
2020
影响因子：
8.6
通讯作者：
Vidmar, Lev
中科院分区：
文献类型：
--
作者：
Łydżba, Patrycja;Rigol, Marcos;Vidmar, Lev
特征态纠缠熵是区分可积量子混沌模型与一般量子混沌模型的有力工具。在可积模型中，平均特征态纠缠熵（在所有哈密顿特征态上）具有通常取决于子系统分数的体积律系数。相反，在量子混沌模型中，它是极大的（子系统分数无关）。利用二次哈密顿算子的随机矩阵理论，我们得到了平均特征态纠缠熵随子系统分数的封闭表达式。我们对二次型Sachdev-Ye-Kitaev模型的数值结果进行了测试，并表明它描述了幂律随机带状矩阵模型（在离域区域）的结果。我们表明，准动量空间中的局部化与我们的分析预测产生（小）偏差。
The eigenstate entanglement entropy is a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, the average eigenstate entanglement entropy (over all Hamiltonian eigenstates) has a volume-law coefficient that generally depends on the subsystem fraction. In contrast, it is maximal (subsystem fraction independent) in quantum-chaotic models. Using random matrix theory for quadratic Hamiltonians, we obtain a closed-form expression for the average eigenstate entanglement entropy as a function of the subsystem fraction. We test it against numerical results for the quadratic Sachdev-Ye-Kitaev model and show that it describes the results for the power-law random banded matrix model (in the delocalized regime). We show that localization in quasimomentum space produces (small) deviations from our analytic predictions.