Interplay of interactions, disorder, and topology in the Haldane-Hubbard model

We investigate the ground-state phase diagram of the spinless Haldane-Hubbard model in the presence of quenched disorder, contrasting results obtained from both exact diagonalization and the density matrix renormalization group, applied to a honeycomb cylinder. The interplay of disorder, interactions, and topology gives rise to a rich phase diagram and, in particular, highlights the possibility of a disorder-driven trivial-to-topological transition in the presence of finite interactions. That is, the topological Anderson insulator, demonstrated in noninteracting settings, is shown to be stable in the presence of sufficiently small interactions before a charge density wave Mott insulator sets in. We further promote a finite-size analysis of the transition to the ordered state in the presence of disorder, finding a mixed character of first- and second-order transitions in finite lattices, tied to the specific conditions of disorder realizations and boundary conditions used.