Łydżba Patrycja, Rigol Marcos, Vidmar Lev
Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia.
Department of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland.
Phys Rev Lett. 2020 Oct 30;125(18):180604. doi: 10.1103/PhysRevLett.125.180604.
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.
本征态纠缠熵是区分可积模型与一般量子混沌模型的有力工具。在可积模型中，平均本征态纠缠熵（对所有哈密顿本征态而言）具有一个体积律系数，该系数通常取决于子系统分数。相比之下，在量子混沌模型中它是最大的（与子系统分数无关）。利用二次哈密顿量的随机矩阵理论，我们得到了作为子系统分数函数的平均本征态纠缠熵的封闭形式表达式。我们将其与二次萨赫德夫 - 叶 - 基塔耶夫模型的数值结果进行对比，结果表明它能够描述幂律随机带状矩阵模型（在离域区域）的结果。我们表明，准动量空间中的局域化会导致与我们的解析预测产生（小的）偏差。
