  Topological phases typically encode topology at the level of the single
particle band structure. But a remarkable class of models shows that quantum
anomalous Hall effects can be driven exclusively by interactions, while the
parent non-interacting band structure is topologically trivial. Unfortunately,
these models have so far relied on interactions that do not spatially decay and
are therefore unphysical. We study a model of spinless fermions on a decorated
honeycomb lattice. Using complementary methods, mean-field theory and exact
diagonalization, we find a robust quantum anomalous Hall phase arising from
spatially decaying interactions. Our finding paves the way for observing the
quantum anomalous Hall effect driven entirely by interactions.
