Wed, Oct 12, 2016, 4:30 pm to 5:30 pm
In this talk I will review some selected aspects of the theory of interacting electrons on the honeycomb lattice, with special emphasis on the Haldane-Hubbard model: this is a model for interacting electrons on the hexagonal lattice, in the presence of nearest and next-to-nearest neighbor hopping, as well as of a transverse dipolar magnetic field. I will discuss the key properties of its phase diagram, most notably the phase transition from a standard insulating phase to a Chern insulator, across a critical line, where the system exhibits semi-metallic behavior. I will also review the universality of its transport coefficients, including the quantization of the transverse conductivity within the gapped phases, and that of the longitudinal conductivity on the critical line. The methods of proof combine constructive Renormalization Group methods with the use of Ward Identities and the Schwinger-Dyson equation. Based on joint works with Vieri Mastropietro, Marcello Porta, Ian Jauslin.