  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.
