研究复杂条件下一维拓扑模型的奇异现象，揭示局域化与拓扑的博弈。
Exploring Topological and Localization Phenomena in SSH Chains under Generalized AAH Modulation: A Computational Approach
- 用数值方法分析广义SSH模型在准周期势下的相图与局域特性。
- 强AAH调制导致边缘态消失，非厄米系统出现皮肤效应全部局域于边界。
- 通过弗洛凯驱动可人工构造拓扑绝缘体，适合研究量子模拟与拓扑材料设计者。
Su-Schrieffer-Heeger（SSH）模型是典型的一维拓扑绝缘体，但其在更复杂、更现实条件下的行为仍是研究热点。本文通过精确对角化与专用数值求解器，系统研究广义SSH模型在准周期无序、非厄米性及时间依赖驱动下的行为。基于谱性质和局域化特征（用逆参与比IPR量化），揭示标准SSH模型的拓扑保护边缘态会被强Aubry-André-Harper（AAH）调制引发的局域化转变破坏。采用主成分分析（PCA）等无监督机器学习方法自动分类系统相态，发现强局域化会掩盖潜在拓扑信号。拓展至非厄米情形，观察到非厄米皮肤效应——所有体态剧烈局域于边界。最后，对拓扑平庸链施加周期弗洛凯驱动，成功构建弗洛凯拓扑绝缘体，其准能带边界出现异常边缘态。这些结果共同呈现了广义一维拓扑系统中丰富的物理现象。
原文摘要 · Abstract (English)
The Su-Schrieffer-Heeger (SSH) model serves as a canonical example of a one-dimensional topological insulator, yet its behavior under more complex, realistic conditions remains a fertile ground for research. This paper presents a comprehensive computational investigation into generalized SSH models, exploring the interplay between topology, quasi-periodic disorder, non-Hermiticity, and time-dependent driving. Using exact diagonalization and specialized numerical solvers, we map the system's phase space through its spectral properties and localization characteristics, quantified by the Inverse Participation Ratio (IPR). We demonstrate that while the standard SSH model exhibits topologically protected edge states, these are destroyed by a localization transition induced by strong Aubry-André-Harper (AAH) modulation. Further, we employ unsupervised machine learning (PCA) to autonomously classify the system's phases, revealing that strong localization can obscure underlying topological signatures. Extending the model beyond Hermiticity, we uncover the non-Hermitian skin effect, a dramatic localization of all bulk states at a boundary. Finally, we apply a periodic Floquet drive to a topologically trivial chain, successfully engineering a Floquet topological insulator characterized by the emergence of anomalous edge states at the boundaries of the quasi-energy zone. These findings collectively provide a multi-faceted view of the rich phenomena hosted in generalized 1D topological systems.
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