Winding number order in the Haldane model with interactions

We study the Haldane model with nearest–neighbor interactions. This model is physically motivated by the associated implementation with ultracold atoms. 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 as a function of the interaction strength.