Machine learning of topological insulator and Anderson insulator in the one-dimensional extended Su-Schrieffer-Heeger chain
Phys. Rev. B 114, 034201 – Published 6 July, 2026
DOI: https://doi.org/10.1103/s26s-gd7v
Abstract
We study disorder effects in the extended Su-Schrieffer-Heeger 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 a chiral-symmetry-preserving off-diagonal disorder system, but fails in the presence of a chiral-symmetry-breaking diagonal disorder system. Using principal component analysis 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 analyses further demonstrate that off-diagonal disorder preserves topological edge states, whereas diagonal disorder drives a transition to an Anderson insulator. Our results show that the out-of-distribution behavior of a CNN trained on clean systems can be understood through the evolution of the RCM feature space under symmetry-preserving and symmetry-breaking disorder, with IPR and energy-spectrum analyses providing the corresponding physical interpretation.