AI 中文总结
该研究针对随机幺正电路建立局域量子信息动力学理论，解析其细粒度结构，发现信息分布的普适标度行为，为连接信息微观理论与流体动力学描述提供了途径。
AI 中文摘要
量子多体系统中信息 scrambling（ scrambling 译为“ scrambling”，此处保留专业术语）的物理性质与热化及混沌的涌现密切相关。然而，通过二分纠缠或算符增长对其进行的标准表征本质上仍属于粗粒化描述，模糊了量子信息如何在系统不同区域之间及不同长度尺度上流动的时空结构。在本研究中，我们针对局域随机幺正电路中的局域信息动力学建立了一套理论，该理论可解析此类系统中局域信息流动的细粒度微观结构。借助信息格（information lattice，用于系统化每个子系统内各长度尺度上信息内容的框架），我们确定了信息所驻留的长度尺度分布，并得到了该分布的动力学。对于具有无限局域希尔伯特空间维数的 Haar 随机电路，我们将该动力学映射为一个精确的经典随机过程，该过程揭示此分布由 Tracy-Widom 形式描述，且该形式随时间以弹道式（∝t）向更大尺度移动，同时伴随~t^(1/3)的展宽。我们还发现，作用于量子比特的随机 Clifford 电路呈现出相同的定性行为。这两种截然不同场景下的相似标度行为强烈暗示了我们结果的普适性。对于 Clifford 电路，我们在特定规范下为 stabilizer 生成元的动力学建立了一个唯象马尔可夫过程，该过程证实了 Tracy-Widom 分布及涨落的 t^(1/3)标度。最终，我们的结果以长度尺度分辨的方式确立了局域量子信息动力学的普适性质，并为弥合信息动力学的精确微观理论与信息流动的涌现流体动力学描述提供了可能的途径。
英文摘要
The physics of information scrambling in quantum many-body systems is intimately related to thermalisation and emergence of chaos. However, its standard characterisation through bipartite entanglement or operator growth remains inherently coarse-grained, obscuring the spatiotemporal anatomy of how quantum information flows between different regions of the system and across various length scales. In this work, we develop a theory for the dynamics of local information in local random unitary circuits which resolves the fine-grained microscopic structures of local information flow in such systems. Using the framework of information lattice which systematises the information content at each length scale within each subsystem, we identify a distribution of length scales at which information resides and obtain the dynamics of the distribution. For Haar-random circuits with infinite local Hilbert-space dimensions, we map this dynamics onto an exact classical stochastic process which reveals that this distribution is described by a Tracy-Widom form which moves ballistically in time ($ \propto t$) toward larger scales, accompanied by a $\sim t^{1/3}$ broadening. We also find the same qualitative behaviour for random Clifford circuits acting on qubits. The similar scaling behaviour in two rather different settings hints strongly towards the universality of our results. In the case of Clifford circuits, we develop a phenomenological Markov process for the dynamics of the stabiliser generators in a specific gauge which confirms the Tracy-Widom distribution and the $t^{1/3}$ scaling of the fluctuations. Ultimately, our results establish the universal properties of the dynamics of local quantum information in a length scale-resolved fashion and provide a possible route towards bridging exact microscopic theories for information dynamics with emergent hydrodynamic descriptions of information flow.
Comments31 pages, 21 figures
