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 as well as 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 non-interacting settings, is shown to be stable to the presence of sufficiently small interactions before a charge density wave Mott insulator sets in. We further perform 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 specific conditions of disorder realizations and boundary conditions used.
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