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 viewpoint 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 nonrandom Floquet models. We also provide an efficient numerical algorithm for determining the entanglement line tension in $1+1\mathrm{D}$.

中文翻译：

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混沌多体系统中的纠缠膜

在某些解析可控的量子混沌系统中，无序相关函数，猝灭后的纠缠熵以及其他相关的动力学可观观测值的计算，简化为时空“纠缠膜”的有效理论。这些易处理的系统涉及定义动态演化的随机局部unit的平均值。我们在这里展示如何在更真实的模型中理解这种膜，该模型不涉及随机unit的平均值。我们的方法依靠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，这是受到随机unit回路中出现的结构的启发。该观点提供了将粗粒度思想应用于混沌系统中的动力学量的框架。我们将这种方法应用于文献中研究的一些平移不变的Floquet自旋链。我们表明，可能为缠结膜定义了一致的线张力，并且通用模型和“双-”电路之间的张力存在质的差异。这些结果允许按比例缩放图片以用于乱序的相关器，并且可以将纠缠从随机电路转移到非随机Floquet模型。我们还提供了一种有效的数值算法来确定缠结线的张力 这些结果允许按比例缩放图片以用于乱序的相关器，并且可以将纠缠从随机电路转移到非随机Floquet模型。我们还提供了一种有效的数值算法来确定缠结线的张力 这些结果允许按比例缩放图片以用于乱序的相关器，并且可以将纠缠从随机电路转移到非随机Floquet模型。我们还提供了一种有效的数值算法来确定缠结线的张力$\mathrm{1个}+\mathrm{1个}\mathrm{d}$。