Christopher Varney, Georgetown
Recent years have seen an explosion of interest in topological phases of matter, which are characterized by robust conducting edge states with the bulk of the material remaining an insulator. In the most well-studied examples of the topologically nontrivial insulators, interactions are considered to be irrelevant and the driving mechanism is a strong spin-orbit coupling or an external magnetic field. However, it has become increasingly important to discover and understand new mechanisms which could stabilize these exotic states of matter. In this talk, I will investigate the signatures of the topological phase transition in interacting systems. The key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the topological transition, even in finite-size systems. I will discuss the theoretical implications of this discovery and utilize exact diagonalization to demonstrate this signature in the Haldane-Fermi-Hubbard model. This result provides a new, efficient way to detect topological transitions in experiments and also in numerical methods that cannot access the ground state wavefunction.