标题： 学习子系统动力学的非马尔可夫特征 显示英文标题

标题： Learning the non-Markovian features of subsystem dynamics

摘要： 量子多体系统中局部可观测量的动力学可以形式化地用开放系统的语言来描述。 问题在于，代表局部子系统补集的环境通常不允许常见的简化，而这些简化对于这种框架通常是至关重要的。 利用张量网络计算和机器学习中的优化工具，我们在全局淬火后，提取并表征了嵌入无限量子伊辛链中的单位点和双位点子系统的动力学映射。 我们考虑了三种典型的区域：可积临界、可积非临界和混沌。 对于每种情况，我们在不同时间找到子系统动力学的最佳时间局部表示。 我们研究了所学的时间依赖李雅普诺夫算子的性质，以及它们是否可用于预测通过直接量子多体数值模拟无法达到的时间之外的局部可观测量的长时间动力学。 我们的方法自然地提出了一种基于准精确动力学映射与最近的CP可分形式之间距离的非马尔可夫性新度量，并揭示了临界性在长时间下导致最接近的马尔可夫表示。 显示英文摘要

摘要： The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common simplifications often crucial for such a framework. Leveraging tensor network calculations and optimization tools from machine learning, we extract and characterize the dynamical maps for single- and two-site subsystems embedded in an infinite quantum Ising chain after a global quench. We consider three paradigmatic regimes: integrable critical, integrable non-critical, and chaotic. For each we find the optimal time-local representation of the subsystem dynamics at different times. We explore the properties of the learned time-dependent Liouvillians and whether they can be used to forecast the long-time dynamics of local observables beyond the times accessible through direct quantum many-body numerical simulation. Our procedure naturally suggests a novel measure of non-Markovianity based on the distance between the quasi-exact dynamical map and the closest CP-divisible form and reveals that criticality leads to the closest Markovian representation at large times.