An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model
An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model
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DOI：
10.1016/j.physleta.2019.126168
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发表时间：
2020-03-09
影响因子：
2.6
通讯作者：
Chiou, Dah-Wei
中科院分区：
文献类型：
--
作者：
Chen, Bo-Hung;Chiou, Dah-Wei
我们概括了包含任意长程跳跃幅度的 Su-Schrieffer-Heeger (SSH) 模型，提供了一个简单的框架来研究任意绝热变形，这些变形在具有任意缠绕数的体能带上保持手性对称性。仅使用求解线性差分方程的基本技术并应用柯西积分公式，我们就获得了广义 SSH 模型的体边界对应关系的数学上严格且物理上透明的证明。稳健的零能量边缘模式的多样性与绕组数相同。另一方面，非零能量边缘模式（如果有的话）在绝热变形下表现出不稳定，并且与拓扑不变量无关。此外，在小空间无序的变形下，零能量边缘模式仍然保持鲁棒性 (C) 2019 Elsevier B.V. 保留所有权利。
We generalize the Su-Schrieffer-Heeger (SSH) model with the inclusion of arbitrary long-range hopping amplitudes, providing a simple framework to investigate arbitrary adiabatic deformations that preserve the chiral symmetry upon the bulk energy bands with any arbitrary winding numbers. Using only elementary techniques of solving linear difference equations and applying Cauchy's integral formula, we obtain a mathematically rigorous and physically transparent proof of the bulk-boundary correspondence for the generalized SSH model. The multiplicity of robust zero-energy edge modes is shown to be identical to the winding number. On the other hand, nonzero-energy edge modes, if any, are shown to be unstable under adiabatic deformations and not related to the topological invariant. Furthermore, under deformations of small spatial disorder, the zero-energy edge modes remain robust (C) 2019 Elsevier B.V. All rights reserved.