多体Floquet模型中Feynman历史的局部配对
Local pairing of Feynman histories in many-body Floquet models
摘要：
我们研究多体量子动力学Floquet量子线路在一个空间维度作为简单的例子，系统与本地相互作用，支持遍历阶段。物理性质可以用费曼历史上的多重和来表示，对于这些模型来说，费曼历史是福克空间中的路径或多体轨道。这种求和的一个自然简化是对角近似，其中保留的唯一项是每条路径与携带复共轭权重的伙伴配对的项。我们确定的制度，其中的对角线近似持有，和性质的领先的更正it. We专注于行为的频谱形状因子（SFF）和矩阵元素的本地运营商，平均在一个合奏的随机电路，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，在很长一段时间内，性能占主导地位的贡献，每个轨道是本地配对的共轭，在对角近似，但在大型系统中，这些贡献包括许多空间域，不同的本地配对在相邻的域。这些领域的存在反映在偏差的SFF从RMT预测，和ETH预测的矩阵元素的相关性;这两种偏差发散与系统的大小。我们表明，我们的轨道配对域的物理图片有一个精确的对应关系，在空间方向上的行为，以产生整体平均的SFF的传输矩阵的光谱特性。此外，我们发现，域的第二种类型的控制非高斯波动的SFF。这些域被与纠缠膜相关的壁分开，已知纠缠膜可以阻止量子信息的扰乱。
英文摘要：
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 behaviour 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 thermalisation 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 neighbouring 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 which are related to the entanglement membrane, known to characterise the scrambling of quantum information.
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