Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges, and anomalous transport properties. In such systems on-site potential disorder, either uncorrelated or incommensurate, is introduced solely at every equally spaced site within the lattice, with a spacing 𝑀≥2. A remarkable property of disordered mosaic lattices is the persistence of extended states at some resonance frequencies that prevent complete Anderson localization, even in the strong disorder regime. Here we introduce a broader class of mosaic lattices and derive general expressions of mobility edges and localization length for incommensurate sinusoidal disorder, which generalize previous results [Y. Wang et al., Phys. Rev. Lett. 125, 196604 (2020).]. For both incommensurate and uncorrelated disorder, we prove that Anderson localization is protected by the open gaps of the disorder-free lattice, and derive some general criteria for complete Anderson localization. The results are illustrated by considering a few models, such as the mosaic Su-Schrieffer-Heeger (SSH) model and the trimer mosaic lattice.

中文翻译：

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广义无序马赛克晶格中的共振、迁移率边缘和间隙保护的 Anderson 定位


马赛克晶格模型最近被引入一类特殊的无序系统，表现出共振能量、多个迁移率边缘和异常传输特性。在这样的系统中，不相关或不相称的位点潜在无序仅在晶格内的每个等距位点引入，间距为 M≥2。无序马赛克晶格的一个显着特性是扩展态在某些共振频率下持续存在，即使在强无序状态下也是如此，这会阻止完全的安德森定位。在这里，我们介绍了一类更广泛的马赛克晶格，并推导出了不相称的正弦无序的迁移率边缘和定位长度的一般表达式，这些表达式概括了以前的结果 [Y. Wang et al.， Phys. Rev. Lett.125， 196604 （2020）。对于不相称和不相关的无序，我们证明了 Anderson 定位受到无序晶格的开放间隙的保护，并推导出了完全 Anderson 定位的一些一般标准。通过考虑一些模型来说明结果，例如马赛克 Su-Schrieffer-Heeger （SSH） 模型和三聚体马赛克晶格。