Kitaev蜂窝模型中的动力学量子相变
Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
摘要：
动态量子相变（DQPT）的概念最近在[Heyl等人，物理修订信函110，135704（2013）]作为在热力学极限中的临界时间处的Loschlord回声的非分析行为。本文研究了二维Kitaev蜂窝模型中DQPT发生时的基态区域的猝灭动力学。对于一般的BCS型的二维系统，它演示了如何在热力学极限的Loschirst回声的零合并到地区，这意味着DQPT发生在二阶导数的不连续性。在Kitaev蜂窝模型中，DQPT出现在猝灭后穿过相边界或在无质量相内。在Kitaev蜂窝模型的一维极限中，很明显，高阶导数的不连续性与非退化模型的高维性密切相关。此外，有一个很强的联系之间的固定值的率函数的Loschirt回波经过很长一段时间后，在这个模型中的DQPT的发生。
英文摘要：
The notion of a dynamical quantum phase transition (DQPT) was recently introduced in [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)] as the non-analytic behavior of the Loschmidt echo at critical times in the thermodynamic limit. In this work the quench dynamics in the ground state sector of the two-dimensional Kitaev honeycomb model are studied regarding the occurrence of DQPTs. For general two-dimensional systems of BCS-type it is demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a phase boundary or within the massless phase. In the 1d limit of the Kitaev honeycomb model it becomes clear that the discontinuity in the higher derivative is intimately related to the higher dimensionality of the non-degenerate model. Moreover, there is a strong connection between the stationary value of the rate function of the Loschmidt echo after long times and the occurrence of DQPTs in this model.
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