Duality between two generalized Aubry-André models with exact mobility edges

Yucheng Wang, Xu Xia, Yongjian Wang, Zuohuan Zheng, Xiong-Jun Liu
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引用次数: 13

Abstract

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 Lyapunov exponents and using the duality relations. Our result may provide insight into realizing and observing exact MEs in both theory and experiment.
具有精确迁移边的两个广义aubry - andr模型之间的对偶性
从局域态扩展的能量分离中的迁移边缘(ME)是理解无序系统中金属-绝缘体跃迁等各种基本现象的中心概念。在一维准周期系统中,存在一些具有精确MEs的模型,这些模型有助于精确理解MEs物理。在这里,我们研究了两种广泛研究的模型,包括精确MEs,一个具有指数跳变和一个具有特殊形式的不相称现场势。分析证明了两种模型是相互对偶的,并通过计算逆参与率和胡思米函数给出了数值验证。通过计算李雅普诺夫指数和利用对偶关系,得到了两种模型的精确MEs。我们的研究结果可以为在理论和实验中实现和观察精确的MEs提供见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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