标题： 周期驱动量子系统中的纠缠不对称性 显示英文标题

标题： Entanglement asymmetry in periodically driven quantum systems

摘要： 我们研究周期驱动量子系统中的纠缠不对称性动力学。 使用一个周期驱动的XY链作为驱动可积量子系统的模型，我们提供了关于纠缠不对称性$\Delta S$随驱动频率变化的动力学行为的半解析结果。 我们的分析确定了特殊的驱动频率，在这些频率下，驱动的XY链表现出动态对称性恢复，并在长时间尺度上显示出量子Mpemba效应；我们发现其Floquet哈密顿量中存在一种涌现的近似对称性，这对实现这两种现象起着关键作用。 我们通过数值计算$\Delta S$对于非可积的驱动里德伯原子链，并在该系统的预热 regime 中获得了由涌现对称性引起的对称性恢复和量子Mpemba效应。 最后，我们提供了对周期驱动的条带上的共形场理论（CFT）的纠缠不对称性的精确解析计算。 这种驱动的CFT，根据驱动振幅和频率的不同，表现出两个不同的相，加热相和非加热相，这两个相由一条临界线分隔。 我们的结果表明，对于周期驱动的$m$周期，时间周期为$T$，在加热相 [临界线上] 的通用 CFT 中，$\Delta S \sim \ln mT$[$\ln (\ln mT)$]；相反，在非加热相中，$\Delta S$随着$mT$的变化在初始值附近显示小振幅振荡。我们提供了驱动 CFT 中$\Delta S$行为的相图，该图是驱动频率和振幅的函数。 显示英文摘要

摘要： We study the dynamics of entanglement asymmetry in periodically driven quantum systems. Using a periodically driven XY chain as a model for a driven integrable quantum system, we provide semi-analytic results for the behavior of the dynamics of the entanglement asymmetry, $\Delta S$, as a function of the drive frequency. Our analysis identifies special drive frequencies at which the driven XY chain exhibits dynamic symmetry restoration and displays quantum Mpemba effect over a long timescale; we identify an emergent approximate symmetry in its Floquet Hamiltonian which plays a crucial role for realization of both these phenomena. We follow these results by numerical computation of $\Delta S$ for the non-integrable driven Rydberg atom chain and obtain similar emergent-symmetry-induced symmetry restoration and quantum Mpemba effect in the prethermal regime for such a system. Finally, we provide an exact analytic computation of the entanglement asymmetry for a periodically driven conformal field theory (CFT) on a strip. Such a driven CFT, depending on the drive amplitude and frequency, exhibits two distinct phases, heating and non-heating, that are separated by a critical line. Our results show that for $m$ cycles of a periodic drive with time period $T$, $\Delta S \sim \ln mT$ [$\ln (\ln mT)$] in the heating phase [on the critical line] for a generic CFT; in contrast, in the non-heating phase, $\Delta S$ displays small amplitude oscillations around it's initial value as a function of $mT$. We provide a phase diagram for the behavior of $\Delta S$ for such driven CFTs as a function of the drive frequency and amplitude.