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.