非互易Maryland模型中的拓扑离域跃迁和迁移率边
Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
摘要：
在准周期晶格中，非厄米效应可以引发光谱、局域化和拓扑相变。我们提出了一个非厄米扩展的马里兰模型，它形成了一个范例，在本地化和量子混沌的研究，通过引入不对称的跳跃幅度。由此产生的非互易马里兰模型被发现拥有一个真正的复杂的频谱过渡在有限数量的跳跃不对称性，通过它从本地化阶段的流动性边缘阶段的变化。得到了复能散、相边界和迁移率边的显式表达式，并引入了拓扑缠绕数来表征不同相之间的转变。我们的工作介绍了一种独特的类型的非厄米准晶体，它承认完全可获得的相图，流动性的边缘，并保持在有限的非互易性在热力学极限没有扩展的阶段。
英文摘要：
Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.
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