Entanglement Membrane in Chaotic Many-Body Systems
Entanglement Membrane in Chaotic Many-Body Systems
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DOI：
10.1103/physrevx.10.031066
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发表时间：
2019-12
期刊：
影响因子：
--
通讯作者：
Tianci Zhou;A. Nahum
中科院分区：
文献类型：
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作者：
Tianci Zhou;A. Nahum
在某些易于分析的量子混沌系统中，对超时序相关函数、猝灭后的纠缠熵和其他相关的动力学观测量的计算，归结为时空中“纠缠膜”的有效理论。这些易处理的系统涉及定义动力学演化的随机局部幺正平均。我们在这里展示了如何在更现实的模型中理解这种膜，这种模型不涉及随机幺正的平均值。我们的方法依赖于在时空中引入有效的配对自由度，描述一对向前和向后的费曼轨迹，灵感来自随机酉电路中出现的结构。这为将粗粒化思想应用于混沌系统中的动力学量提供了一个框架。我们将这种方法应用于文献中研究的一些几何不变的Floquet自旋链。我们表明，一个一致的线张力可以被定义为纠缠膜，并且有质的差异，在这种紧张之间的通用模型和“双酉”电路。这些结果允许缩放图片的时间顺序的离散和纠缠被接管从随机电路到非随机Floquet模型。我们还提供了一个有效的数值算法来确定1+ 1维纠缠线的张力。
In certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables, reduces to an effective theory of an ``entanglement membrane'' in spacetime. These tractable systems involve an average over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries. Our approach relies on introducing effective pairing degrees of freedom in spacetime, describing a pairing of forward and backward Feynman trajectories, inspired by the structure emerging in random unitary circuits. This provides a framework for applying ideas of coarse-graining to dynamical quantities in chaotic systems. We apply the approach to some translationally invariant Floquet spin chains studied in the literature. We show that a consistent line tension may be defined for the entanglement membrane, and that there are qualitative differences in this tension between generic models and ``dual-unitary'' circuits. These results allow scaling pictures for out-of-time-order correlators and for entanglement to be taken over from random circuits to non-random Floquet models. We also provide an efficient numerical algorithm for determining the entanglement line tension in 1+1D.