Recent experimental and theoretical works have made much progress toward understanding nonequilibrium phenomena in thermalizing systems, which act as thermal baths for their small subsystems, and many-body localized systems, which fail to do so. The description of time evolution in many-body systems is generally challenging due to the dynamical generation of quantum entanglement. In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics. The central object in our approach is the influence matrix, which describes the effect of the system on the dynamics of a local subsystem. For translationally invariant models, we formulate a self-consistency equation for the influence matrix. For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin. For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the influence matrix temporal entanglement is low. A combination of analytical insights and MPS computations allows us to characterize the structure of the influence matrix in terms of an effective “statistical-mechanics” description. We finally illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The influence matrix approach formulated here provides an intuitive view of the quantum many-body dynamics problem, opening a path to constructing models of thermalizing dynamics that are solvable or can be efficiently treated by MPS-based methods and to further characterizing quantum ergodicity or lack thereof.

中文翻译：

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影响矩阵法的多体浮球动力学

最近的实验和理论工作在理解热化系统中的非平衡现象方面取得了很大进展，热化系统是其小型子系统的热浴，而多体本地化系统则不能这样做。由于量子纠缠的动态产生，因此在多体系统中对时间演化的描述通常具有挑战性。在这项工作中，我们介绍了一种在费曼-弗农影响函数的启发下研究量子多体动力学的方法。着眼于相互作用的Floquet自旋链族，我们考虑动力学的Keldysh路径积分描述。我们方法的中心对象是影响矩阵，它描述了系统对局部子系统动力学的影响。对于平移不变模型，我们为影响矩阵制定了一个自洽方程。对于模型参数的某些特殊值，我们获得了代表完美的移相器（PD）的精确解。从物理上讲，局部放电对应于一个多体系统，可以在其自身上充当完美的马尔可夫浴：在每个周期中，它都会测量每次旋转。对于此处考虑的模型，我们确定PD点包括最近工作中研究的双-电路。在PD点附近，该系统并非完美的马尔可夫模型，而是充当了具有较短存储时间的浴池。在这种情况下，我们证明了自洽方程可以使用矩阵乘积状态（MPS）方法求解，因为影响矩阵的时间纠缠很小。分析见解和MPS计算相结合，使我们能够根据有效的“统计力学”描述来表征影响矩阵的结构。我们最后通过分析计算嵌入的杂质自旋热化的速度来说明此描述的预测能力。本文制定的影响矩阵方法可直观地了解量子多体动力学问题，为构建可解决的或可通过基于MPS的方法有效处理的热动力学模型，以及进一步表征量子遍历性或缺乏量子遍历性开辟了道路。