算子瑞尼熵与非相互作用系统中算子增长和纠缠增长的施温格尔-凯尔迪什场论
Schwinger-Keldysh field theory for operator Rényi entropy and entanglement growth in non-interacting systems with sub-ballistic transports
AI总结：
该研究利用施温格尔-凯尔迪什场论，探讨非相互作用系统中算子增长与纠缠增长及传输行为的关系。
摘要：
量子系统中算子增长的概念为传输和量子动力学下系统不同部分之间纠缠的生成提供了桥梁。我们定义了算子增长的度量，即子系统算子瑞尼熵，它提供了一个与状态无关的算子增长度量，不同于纠缠熵和通常的算子增长度量，如时间序反序相关子。我们证明子系统算子瑞尼熵编码了空间和时间信息，因此可以直接连接到与守恒量相关的局部算子的传输。我们构建了一个统一的施温格尔-凯尔迪什（SK）场论形式化，用于初始纯态的算子瑞尼熵和纠缠熵的时间演化。我们使用SK场论以无限温度和真空凯尔迪什格林函数分别获得非相互作用系统的算子瑞尼熵和态纠缠熵。我们应用该方法探索算子和纠缠增长与非相互作用系统中准周期性和随机无序（如一维和二维 Aubry-André 模型和二维 Anderson 模型）传输之间的联系。特别是，我们展示了子系统算子瑞尼熵和态 von Neumann 和瑞尼纠缠熵的增长可以捕捉到这些系统中的球形和亚球形传输行为，如扩散和异常扩散传输，以及局部化。
英文摘要：
The notion of operator growth in quantum systems furnishes a bridge between transport and the generation of entanglement between different parts of the system under quantum dynamics. We define a measure of operator growth in terms of subsystem operator Rényi entropy, which provides a state-independent measure of operator growth, unlike entanglement entropies, and the usual measures of operator growth like out-of-time-order correlators. We show that the subsystem operator Rényi entropy encodes both spatial and temporal information, and thus can directly connect to transport for a local operator related to a conserved quantity. We construct a unified Schwinger-Keldysh (SK) field theory formalism for the time evolution of operator Rényi entropy and entanglement entropies of initial pure states. We use the SK field theory to obtain the operator Rényi and state entanglement entropies in terms of infinite-temperature and vacuum Keldysh Green's functions, respectively, for non-interacting systems. We apply the method to explore the connection between operator and entanglement growth, and transport in non-interacting systems with quasiperiodic and random disorder, like the one- and two-dimensional Aubry-André models and the two-dimensional Anderson model. In particular, we show that the growth of subsystem operator Rényi entropy and state von Neumann and Rényi entanglement entropies can capture both ballistic and sub-ballistic transport behaviors, like diffusive and anomalous diffusive transport, as well as localization in these systems.
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