发表机构
Institute of Physics, Chinese Academy of Sciences; Department of Physics, Princeton University; Graduate School of China Academy of Engineering Physics（中国科学院物理研究所; 普林斯顿大学物理系; 中国工程物理研究院研究生院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出施密特尺度坐标作为动力学探针，揭示纠缠增长中熵产生、谱重组与主导尺度输运的层级时序及其物理起源。
AI 中文摘要
量子纠缠增长通常通过单一熵来概括，这掩盖了相关性在指数级大的施密特谱中的位置及其形成方式。在此，我们引入施密特尺度集中度和主导施密特尺度这两个坐标，它们用于在有序施密特秩空间的对数窗口中定位概率最大值。将这些坐标应用于随机场自旋链的淬火过程，这些坐标能够区分弱无序下主导尺度向更高施密特秩的快速输运与强无序下尽管对数熵持续增长但输运被强烈抑制的情况。无序平均动力学展现出有序的层级结构：熵产生首先达到峰值，谱粗糙度和精确非局域魔法其次达到峰值，而主导施密特尺度输运仅在显著延迟后才变得典型。此外，一个可解的头部-尾部模型和受控数值实验揭示了这一层级结构的物理起源：谱路径决定了事件的顺序，活跃交换键上的局域动力学设定了它们的早期时序，而子系统内部的多体修饰进一步延迟了主导施密特尺度输运。这些结果确立了施密特尺度坐标作为强大的动力学探针，用于揭示超越单一熵的精细纠缠结构，区分纠缠产生、纠缠谱重组和主导施密特尺度输运。
英文摘要
Quantum entanglement growth is commonly summarized by a single entropy, obscuring where correlations reside in the exponentially large Schmidt spectrum and how they form. Here, we introduce Schmidt-scale concentration and dominant Schmidt scale, two coordinates that locate the probability maximum across logarithmic windows in ordered Schmidt-rank space. Applied to quenches of a random-field spin chain, these coordinates distinguish rapid transport of the dominant scale to higher Schmidt rank at weak disorder from strongly suppressed transport despite continued logarithmic entropy growth at strong disorder. The disorder-averaged dynamics exhibit an ordered hierarchy: entropy production peaks first, spectral roughness and exact nonlocal magic peak next, and dominant-Schmidt-scale transport becomes typical only after a substantial delay. Moreover, a solvable head--tail model and controlled numerical experiments reveal the physical origin of this hierarchy: the spectral path determines the order of events, local dynamics on active exchange bonds set their early timing, and intra-subsystem many-body dressing further delays dominant-Schmidt-scale transport. These results establish the Schmidt-scale coordinates as powerful dynamical probes for uncovering fine-grained entanglement structures distinguishing entanglement production, entanglement-spectrum reorganization, and dominant-Schmidt-scale transport beyond entropy alone.
Comments4.5 pages, 3 figures, with references and supplemental materials
