Quantum Simulation of a Topological Mott Insulator with Rydberg Atoms in a Lieb Lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase - an interaction-driven topological insulator - using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest and next-to-nearest neighbor interactions, and derive the associated zero temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic as well as a topologically non-trivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access in particular the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques.