从平衡态相变中分离动力学相变
Disentangling dynamical phase transitions from equilibrium phase transitions
摘要：
动态相变（DPT）发生在量子系统中的一些全局参数猝灭之后，并且通过动态自由能的非解析时间演化来表示，该动态自由能是从初始状态和时间演化状态之间的Loschlord重叠计算的。在最近的一封信中（M。Heyl等人，物理修订信函\textbf{110}，135704（2013）），提出了DPT与横向场伊辛模型的平衡相变（EPT）密切相关。通过研究横向磁场中的XY链这一极小模型，我们用解析的方法证明了这种联系并不普遍成立。我们提出的例子中，DPT发生而不交叉任何平衡临界线的淬火，和一个不平凡的例子，没有DPT，但交叉临界线的淬火。虽然在实时间轴上的动力学自由能的非解析性并不表明EPT的存在或不存在，但复杂时间的Fisher线结构揭示了质的差异。
英文摘要：
Dynamical phase transitions (DPT) occur after quenching some global parameters in quantum systems and are signalled by the non-analytical time evolution of the dynamical free energy, which is calculated from the Loschmidt overlap between the initial and time evolved states. In a recent letter (M. Heyl et al., Phys. Rev. Lett. \textbf{110}, 135704 (2013)), it was suggested that DPTs are closely related to equilibrium phase transitions (EPT) for the transverse field Ising model. By studying a minimal model, the XY chain in transverse magnetic field, we show analytically that this connection does not hold generally. We present examples where DPT occurs without crossing any equilibrium critical lines by the quench, and a nontrivial example with no DPT but crossing a critical line by the quench. Albeit the non-analyticities of the dynamical free energy on the real time axis do not indicate the presence or absence of an EPT, the structure of Fisher-lines for complex times reveal a qualitative difference.
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