AI 中文总结
本研究在周期性驱动的Ising链中发现两个时间纠缠转变可合并为临界接触，实现连续相变的时间类比，并揭示了其非解析特征与Floquet机制。
AI 中文摘要
平衡相变通常被分类为一阶相变和连续相变。远离平衡态时，在量子系统的实时演化过程中会出现许多新的转变。其中一种转变是时间纠缠转变（TET），其特征是纠缠谱的非解析性。到目前为止，所有TET都是通过不同对称性扇区中领先Schmidt能级的线性交叉发生的，类似于平衡态中的一阶转变。一个自然的问题是，以纠缠谱接触为特征的连续TET是否可能。在周期性驱动的横向$J_1$-$J_2$ Ising链中，我们展示了两个这样的TET可以合并成一个临界接触，其中领先能级切向相遇而不交换，实现了连续相变的时间类比。在临界频率附近，两个TET的时间间隔连续消失，其相对于频率的导数发散，这是单个一阶TET中不存在的非解析特征。这种有限频率接触源于乘积初态的弱对称保持微扰与Floquet修正之间的相互作用。进一步扩展频率扫描揭示了在更高频率处存在第二个临界接触，并且两个临界频率包围了一个没有TET的有限窗口。这些特征可以从二阶Floquet哈密顿量理解，并在广泛的耦合比范围内持续存在，从而将临界接触确立为TET的一种独特形式。
英文摘要
Equilibrium phase transitions are conventionally categorized into first-order and continuous phase transitions. Far from equilibrium, many new transitions emerge during the real-time evolution of quantum systems. One such transition is the temporal entanglement transition (TET) characterized by the nonanalyticity of the entanglement spectrum. So far, all TETs occur through a linear crossing of the leading Schmidt levels in different symmetry sectors, resembling a first-order transition in equilibrium. A natural question is whether a continuous TET, featured by entanglement spectrum touching, is possible. In a periodically driven transverse $J_1$-$J_2$ Ising chain, we show that two such TETs can merge into a critical touching, where the leading levels meet tangentially without exchanging, realizing the temporal analog of a continuous phase transition. Near the critical frequency, the temporal separation of the two TETs vanishes continuously and its derivative with respect to frequency diverges, a nonanalytic signature that is absent in a single first-order TET. This finite-frequency touching arises from the interplay between a weak symmetry-preserving perturbation of the product initial state and Floquet corrections. Further extending the frequency scan reveals a second critical touching at a higher frequency, and the two critical frequencies enclose a finite window with no TET. These features can be understood from a second-order Floquet Hamiltonian and persist across a broad range of coupling ratios, establishing the critical touching as a distinct form of TET.
Comments4.5 pages, 3 figures + supplemental material
