Operator entanglement entropy of the time evolution operator in chaotic systems
Operator entanglement entropy of the time evolution operator in chaotic systems
复制标题
混沌系统中时间演化算子的算子纠缠熵
DOI：
10.1103/physrevb.95.094206
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发表时间：
2016
影响因子：
3.7
通讯作者：
D. J. Luitz
中科院分区：
文献类型：
--
作者：
Tianci Zhou;D. J. Luitz
纠缠熵是量子混沌开始的一个广泛适用的指标。特别地，从具有低纠缠的初始态猝灭后的波函数的纠缠熵可以用于研究系统的热化。在这里，作者提出了一个称为“算符纠缠熵”（opEE）的初始状态独立量，以提取酉演化算符的属性。他们研究Floquet，混沌和多体局部系统中opEE的增长。它们在达到广泛的饱和值之前分别有线性、幂律和对数增长。最混乱的Floquet自旋模型具有三个类别中的最大饱和值，并且与随机酉算子的值（Page值）相同。作者将opEE解释为双希尔伯特空间中猝灭态的态EE，从而建立了与现有态EE结果的一致性。他们的结论是，进化算子的EE应该表征这些系统中信息的传播。
Entanglement entropy is a widely applicable indicator of the onset of quantum chaos. In particular, the entanglement entropy of the wave function after a quench from an initial state with low entanglement can be used to study the thermalization of the system. Here, the authors propose an initial-state independent quantity called the ``operator entanglement entropy'' (opEE) to extract the properties of the unitary evolution operator. They study the growth of the opEE in Floquet, chaotic, and many-body localized systems. They respectively have a linear, power-law, and logarithmic growth before reaching extensive saturation values. The most chaotic Floquet spin model has the maximal saturation value among the three classes and is identical to the value of a random unitary operator (the Page value). The authors interpret the opEE as the state EE of a quenched state living in a doubled Hilbert space, thus establishing its consistency with the existing state EE results. They conclude that the EE of the evolution operator should characterize the propagation of information in these systems.