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arXiv:2605.27524

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

Alejandro José Uría-Álvarez, Roser Valentí

Published May 26, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2605.27524

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We study the ground-state phase diagram of the half-filled extended Haldane-Hubbard model on the honeycomb lattice with sublattice-dependent on-site repulsion (UA/B{U}_{\text{A/B}}UA/B​) using the exact diagonalization (ED) and mean-field (MF) methods. The resulting phase diagram shows that there is a topologically nontrivial phase with the Chern number C=1C=1C=1, emerging via the development of the imbalance between UA{U}_{\text{A}}UA​ and UB{U}_{\text{B}}UB​. In this phase, the antiferromagnetic correlations are observed in the ED calculation, in line with the finite antiferromagnetic order obtained by the MF method. The spontaneous symmetry breaking of SU(2) spin rotation in the phase is also identified in the MF level. Distinct from previous studies in which the exotic C=1C=1C=1 phase relies on the interplay between sublattice-dependent potentials and electronic interactions, our paper presents an alternative way by solely tuning the on-site interactions.
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Using dynamical mean-field theory and exact diagonalization we study the phase diagram of the repulsive Haldane-Hubbard model, varying the interaction strength and the sublattice potential difference. In addition to the quantum Hall phase with Chern number C=2 and the band insulator with C=0 present already in the noninteracting model, the system also exhibits a C=0 Mott insulating phase, and a C=1 quantum Hall phase. We explain the latter phase by a spontaneous symmetry breaking where one of the spin components is in the Hall state and the other in the band insulating state.