Eigenstate Correlations, the Eigenstate Thermalization Hypothesis, and Quantum Information Dynamics in Chaotic Many-Body Quantum Systems,Physical Review X

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Eigenstate Correlations, the Eigenstate Thermalization Hypothesis, and Quantum Information Dynamics in Chaotic Many-Body Quantum Systems
Physical Review X ( IF 11.6 ) Pub Date : 2024-08-16 , DOI: 10.1103/physrevx.14.031029
Dominik Hahn ₁ , David J. Luitz ₂ , J. T. Chalker ₃

Affiliation

We consider the statistical properties of eigenstates of the time-evolution operator in chaotic many-body quantum systems. Our focus is on correlations between eigenstates that are specific to spatially extended systems and that characterize entanglement dynamics and operator spreading. In order to isolate these aspects of dynamics from those arising as a result of local conservation laws, we consider Floquet systems in which there are no conserved densities. The correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalization hypothesis (ETH). In particular, ETH provides a statistical description of matrix elements of local operators between pairs of eigenstates, whereas the aspects of dynamics we are concerned with arise from correlations among sets of four or more eigenstates. We establish the simplest correlation function that captures these correlations and discuss features of its behavior that are expected to be universal at long distances and low energies. We also propose a maximum-entropy ansatz for the joint distribution of a small number n of eigenstates. In the case n=2, this ansatz reproduces ETH. For n=4 it captures both the growth with time of entanglement between subsystems, as characterized by the purity of the time-evolution operator, and also operator spreading, as characterized by the behavior of the out-of-time-order correlator. We test these ideas by comparing results from Monte Carlo sampling of our ansatz with exact diagonalization studies of Floquet quantum circuits.

Published by the American Physical Society

2024

中文翻译：

混沌多体量子系统中的特征态相关性、特征态热化假说和量子信息动力学

我们考虑了混沌多体量子系统中时间演化算子特征态的统计特性。我们的重点是空间扩展系统特有的特征态之间的相关性，这些特征表征了纠缠动力学和算子扩散。为了将这些动力学方面与当地守恒定律产生的动力学方面隔离开来，我们考虑了没有守恒密度的 Floquet 系统。与量子信息加扰相关的相关性位于本征态热化假说（ETH）建立的标准框架之外。特别是，ETH 提供了对特征态对之间局部算子矩阵元素的统计描述，而我们关注的动力学方面则来自四个或更多特征态集合之间的相关性。我们建立了最简单的相关函数来捕获这些相关性，并讨论了其行为特征，这些特征预计在长距离和低能量下是普遍的。我们还提出了一个最大熵拟设，用于少量 n 个特征态的联合分布。在 n=2 的情况下，此拟设复制 ETH。当 n=4 时，它既捕获子系统之间纠缠随时间的增长（以时间演化算子的纯度为特征），也捕获算子扩散（以非时间顺序相关器的行为为特征）。我们通过将拟设的蒙特卡洛采样结果与 Floquet 量子电路的精确对角化研究的结果进行比较来测试这些想法。美国物理学会 2024 年出版

更新日期：2024-08-16

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