Machine Learning of Topological Insulator and Anderson Insulator in One-Dimensional Extended Su-Schrieffer-Heeger Chain

TL;DR

This paper employs machine learning, specifically CNNs and PCA, to analyze disorder effects in the extended SSH model, revealing how different disorders influence topological phases and transitions to Anderson insulators.

Contribution

It introduces a CNN-based method to predict topological phase diagrams in disordered systems and analyzes symmetry effects using PCA, IPR, and energy spectra.

Findings

CNN accurately predicts phase diagrams in symmetry-preserving disorder

Symmetry-breaking disorder leads to divergence in feature space

Off-diagonal disorder preserves topological edge states

Abstract

We study disorder effects in the extended Su-Schrieffer-Heeger (SSH) model using a convolutional neural network (CNN) trained on reduced correlation matrices (RCMs) of disorder-free systems to predict winding number phase diagrams in systems with off-diagonal and diagonal disorder. The trained CNN model generalizes to chiral-symmetry-preserving off-diagonal disorder system but fails in the presence of chiral-symmetry-breaking diagonal disorder system. Using principal component analysis (PCA) of the RCM feature space, we demonstrate that disorder-free and symmetry-preserving systems share overlapping feature manifolds, whereas symmetry-breaking disorder causes them to diverge. Inverse participation ratio (IPR) and energy spectrum analysis further demonstrate that off-diagonal disorder preserves topological edge states, whereas diagonal disorder drives a transition to an Anderson insulator. Our results position machine learning not merely as a classifier, but as a sensitive probe for the symmetry-protected nature of quantum matter.