不动点、Floquet纠缠不对称性与量子Mpemba效应
Fixed Points, Floquet Entanglement Asymmetry, and Quantum Mpemba Effects
- Saha Institute of Nuclear Physics（萨哈核物理研究所）
- Homi Bhabha National Institute（霍米·巴巴国立研究所）
- SISSA（的里雅斯特高等研究学院）
- INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文通过共形映射（特别是Möbius映射）的不动点结构，统一描述了周期驱动二维共形场论中纠缠不对称性的动力学，揭示了局域对称性恢复、量子Mpemba效应及其逆效应的几何机制。
中文摘要 AI 辅助
我们利用基于迭代共形映射（特别是Möbius映射）的动力系统描述，研究了具有全局U(1)对称性的周期驱动二维共形场论中纠缠不对称性的动力学。从由局域算符插入制备的对称性破缺激发态出发，我们表明广泛的非平衡现象，包括局域对称性恢复、量子Mpemba效应及其逆效应，都可以用共形映射的不变数据给出简单的几何描述。我们使用Möbius映射明确证明了这一点，其不变结构由共轭类描述。特别是，纠缠不对称性的动力学由态制备算符插入点、子系统和不动点的相对位置决定，从而产生增长、衰减、振荡和饱和的不同模式。我们进一步论证，这种几何图像可以推广到一般的全纯映射，从而确立共形映射动力学作为组织周期驱动二维共形场论中纠缠不对称性现象学的自然框架。
英文摘要
We investigate the dynamics of entanglement asymmetry in periodically driven two-dimensional conformal field theories with a global U$(1)$ symmetry, using a dynamical-system description based on iterated conformal maps, in particular Möbius maps. Starting from a symmetry-breaking excited state prepared by a local operator insertion, we show that a broad range of nonequilibrium phenomena, including local symmetry restoration, the quantum Mpemba effect, and its inverse, admit a simple geometric description in terms of the invariant data of the conformal map. We explicitly demonstrate this using Möbius maps, for which the invariant structure is described by the conjugacy classes. In particular, the dynamics of entanglement asymmetry is determined by the relative positions of the state-preparing operator insertion, the subsystem, and the fixed points, yielding distinct patterns of growth, decay, oscillation, and saturation. We further argue that this geometric picture extends to general holomorphic maps, establishing the conformal-map dynamics as a natural framework for organizing the phenomenology of entanglement asymmetry in periodically driven two-dimensional conformal field theories.
