Abstract

In the last few years there has been important progress on the rigorous understanding of the stability of gapped topological phases for interacting condensed matter systems. Most of the available results deal with bulk transport, for systems with no boundaries. In this talk, I will consider interacting 2d topological insulators on the cylinder. According to the bulk-edge duality, one expects robust gapless edge modes to appear. By now, this has been rigorously understood for a wide class of noninteracting topological insulators; the main limitation of all existing proofs is that they do not extend to interacting systems. In this talk I will discuss the bulk-edge duality for a class of interacting 2d topological insulators, including the Haldane-Hubbard model and the Kane-Mele-Hubbard model. Our theorems give a precise characterization of edge transport: besides the bulk-edge duality, the interacting edge modes satisfy the Haldane relations, connecting the velocities of the edge currents, the edge Drude weights and the edge susceptibilities. The proofs are based on rigorous renormalization group, with key nonperturbative inputs coming from the combination of lattice and emergent Ward identities. Based on joint works with G. Antinucci (Zurich) and V. Mastropietro (Milan).