论文标题
具有精确移动性边缘的两个广义Aubry-Andre模型之间的二元性
Duality between two generalized Aubry-Andre models with exact mobility edges
论文作者
论文摘要
从局部状态延伸的能量中的流动性边缘（ME）是理解各种基本现象（如无序系统中的金属 - 绝缘体过渡）的核心概念。在一维准膜系统中，存在一些具有精确ME的模型，这些模型有益于对我物理学的确切理解。在这里，我们研究了两个广泛研究的模型，包括精确的ME，一个具有指数跳跃的模型，另一个具有特殊形式的现场电位。我们在分析上证明了这两个模型是相互双重的，并通过计算反向参与率和HUSIMI函数进一步提供了数值验证。还通过计算定位长度和使用二元关系来获得两个模型的确切ME。我们的结果可能会提供有关在理论和实验中实现和观察精确ME的见解。
A mobility edge (ME) in energy separating extended from localized states is a central concept in understanding various fundamental phenomena like the metal-insulator transition in disordered systems. In one-dimensional quasiperiodic systems, there exist a few models with exact MEs, and these models are beneficial to provide exact understanding of ME physics. Here we investigate two widely studied models including exact MEs, one with an exponential hopping and one with a special form of incommensurate on-site potential. We analytically prove that the two models are mutually dual, and further give the numerical verification by calculating the inverse participation ratio and Husimi function. The exact MEs of the two models are also obtained by calculating the localization lengths and using the duality relations. Our result may provide insight into realizing and observing exact MEs in both theory and experiment.
