Cold-atom regularizations of strongly-coupled four-Fermi field theories in 2+1 dimensions

In this talk, I will disucss how ultra-cold atoms with synthetic spin-orbit coupling in Raman lattices can be used as versatile quantum simulators of strongly-coupled four-Fermi field theories related to Gross-Neveu-Wilson models in (2+1) dimensions. I will present  large-N results that support the appearance of a quantum anomalous Hall (QAH) effect associated to a correlated topological insulator, the boundaries of which are controlled by strongly-coupled fixed points of the four-Fermi relativistic field theory.  In the strong coupling limit, this lattice model  maps onto a two-dimensional quantum compass model in a transverse field, which can be studied using a variational ansatz based on projected entangled pairs.