Interaction-driven Topological Phase Transitions in Fermionic and Dipolar Topological Insulators

While topological invariants are well-known in many free fermion systems, it is often challenging to diagnose topological phases in the presence of interactions. Here, we investigate the topological phase transitions in a strongly interacting one-dimensional fermionic topological insulator (TI) in the presence of three types of interactions: an inter- and intra-cell dipolar interactions V_g and V_h, and an on-site density-density interaction $\tilde{U}$. We propose a set of topological invariants {κ} based on fermionic and dipolar Greens functions, which can diagnose phase transitions in both the fermionic and dipolar sectors. By calculating {κ} using Exact Diagonalization, we find a rich topological phase diagram where the competition between V_g and V_h switches on and off a dipolar TI phase, and $\tilde{U}$ further drives topological phase transitions in both the fermionic and dipolar sectors. The resulting phase diagram is consistent with that obtained by identifying the presence of fermionic and dipolar boundary modes. Finally, I will discuss the divergences and zeros in the fermionic and dipolar Greens functions at the phase transitions in our model.