Topological phases in the Haldane model with spin-spin on-site interactions

Ultracold atom experiments allow the study of topological insulators, such as the non-interacting Haldane model. In this work we study a generalization of the Haldane model with spin-spin on-site interactions that can be implemented on such experiments. We focus on measuring the winding number, a topological invariant, of the ground state, which we compute using a mean-field calculation that effectively captures long-range correlations and a matrix product state computation in a lattice with 64 sites. Our main result is that we show how the topological phases present in the non-interacting model survive until the interactions are comparable to the kinetic energy. We also demonstrate the accuracy of our mean-field approach in efficiently capturing long-range correlations. Based on state-of-the-art ultracold atom experiments, we propose an implementation of our model that can give information about the topological phases.