Exploring Topological and Localization Phenomena in SSH Chains under Generalized AAH Modulation: A Computational Approach

TL;DR

This study computationally explores how generalized SSH chains exhibit complex topological and localization phenomena under various modulations, revealing phase transitions, non-Hermitian effects, and Floquet topological states.

Contribution

It introduces a comprehensive computational framework analyzing the interplay of topology, disorder, non-Hermiticity, and periodic driving in generalized SSH models, including machine learning classification.

Findings

Localization transition induced by strong AAH modulation destroys edge states.

Non-Hermitian skin effect causes bulk state localization at boundaries.

Periodic Floquet driving induces topological edge states in trivial chains.

Abstract

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-Andr\'e-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.