We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many-body orbits in Fock space. A natural simplification of such sums is the diagonal approximation, where the only terms that are retained are ones in which each path is paired with a partner that carries the complex conjugate weight. We identify the regime in which the diagonal approximation holds and the nature of the leading corrections to it. We focus on the behavior of the spectral form factor (SFF) and of matrix elements of local operators, averaged over an ensemble of random circuits, making comparisons with the predictions of random matrix theory (RMT) and the eigenstate thermalization hypothesis (ETH). We show that properties are dominated at long times by contributions to orbit sums in which each orbit is paired locally with a conjugate, as in the diagonal approximation, but that in large systems these contributions consist of many spatial domains, with distinct local pairings in neighboring domains. The existence of these domains is reflected in deviations of the SFF from RMT predictions, and of matrix element correlations from ETH predictions; deviations of both kinds diverge with system size. We demonstrate that our physical picture of orbit-pairing domains has a precise correspondence in the spectral properties of a transfer matrix that acts in the space direction to generate the ensemble-averaged SFF. In addition, we find that domains of a second type control non-Gaussian fluctuations of the SFF. These domains are separated by walls that are related to the entanglement membrane, known to characterize the scrambling of quantum information.

中文翻译：

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多体 Floquet 模型中费曼历史的局部配对

我们在一维空间中使用 Floquet 量子电路研究多体量子动力学，作为具有支持遍历阶段的局部相互作用的系统的简单示例。物理属性可以用费曼历史上的多个总和来表示，对于这些模型来说，它们是福克空间中的路径或多体轨道。这种总和的自然简化是对角线近似，其中唯一保留的项是其中每条路径都与带有复共轭权重的伙伴配对的项。我们确定了对角线近似的适用范围以及对其进行主要修正的性质。我们专注于频谱形状因子 (SFF) 和本地运算符的矩阵元素的行为，在随机电路的集合上平均，与随机矩阵理论 (RMT) 和本征态热化假设 (ETH) 的预测进行比较。我们表明，性质在长时间内主要由对轨道总和的贡献决定，其中每个轨道局部与共轭配对，如对角线近似，但在大型系统中，这些贡献由许多空间域组成，相邻的局部配对不同域。这些域的存在反映在 SFF 与 RMT 预测的偏差，以及矩阵元素相关性与 ETH 预测的偏差；两种偏差都随着系统规模而发散。我们证明了我们的轨道配对域的物理图片在传递矩阵的光谱属性中具有精确的对应关系，该矩阵在空间方向上起作用以生成整体平均 SFF。此外，我们发现第二种类型的域控制 SFF 的非高斯波动。这些域被与纠缠膜相关的壁隔开，纠缠膜是量子信息加扰的特征。