  We study the Haldane model with nearest-neighbor interactions. This model is
physically motivated by the associated ultracold atoms implementation. We show
that the topological phase of the interacting model can be characterized by a
physically observable winding number. The robustness of this number extends
well beyond the topological insulator phase towards attractive and repulsive
interactions that are comparable to the kinetic energy scale of the model. We
identify and characterize the relevant phases of the model.
