Topological analysis of the complex SSH model using the quantum geometric tensor

TL;DR

This paper introduces two methods, Berry phase and topological data analysis, to analyze the topological phases of the complex SSH model, revealing trivial and non-trivial regions based on parameter ratios.

Contribution

It presents a novel application of quantum geometric tensor methods to topologically analyze the complex SSH model, aiding future studies of similar systems.

Findings

Identified topologically trivial phase when |v| > |w|.

Identified topologically non-trivial phase when |v| < |w|.

Demonstrated effective phase diagram generation for the complex SSH model.

Abstract

This paper presents two methods for topological analysis of the complex Hermitian Su-Schrieffer-Heeger (SSH) model using the quantum geometric tensor: Berry phase and topological data analysis. We demonstrate how both methods can effectively generate topological phase diagrams for the model, revealing two distinct regions based on the relative magnitudes of the parameters $|v|$ and $|w|$. Specifically, when $|v| > |w|$, the system is found to be topologically trivial, whereas for $|v| < |w|$, it exhibits topologically non-trivial behavior. Our results contribute to building the groundwork for topological analysis of more complicated SSH-type models.