Emergence of an antiferromagnetic topological Anderson insulator in the interacting Haldane model

Abstract

We examine the emergence of topological Anderson insulating phases in the spinful Haldane model with Hubbard and next-neighbor density-density interactions, subject to Anderson disorder. Using finite-size exact diagonalization, we characterize the phases that arise from the interplay between topology, interactions, and disorder. In addition to standard $C=2$ topological Anderson phases, we observe an antiferromagnetic $C=1$ topological Anderson phase, consistent with the antiferromagnetic quantum anomalous Hall insulator previously identified in the clean model at finite staggered mass. We further analyze these phases using a neural network trained on the exact diagonalization data. Our results support the hypothesis that an explicit charge imbalance is required to induce the $C=1$ phase, generated by Anderson disorder rather than by a staggered mass.