The quantum anomalous Hall effect can, in principle, be driven entirely by interparticle interactions into a new phase of matter called the topological Mott insulator. Calculations to date have shown that this effect can arise in simple models only when the interaction strength between particles is not spatially decaying. Such interactions are typically unphysical. Here, the authors study particles in a decorated honeycomb lattice to find that spatially decaying interactions do in fact lead to a topological Mott insulator with a quantum anomalous Hall effect. The results set the stage for realizing interaction-driven topological effects in quantum matter.
We show that the decorated honeycomb (star) lattice supports a number of topological insulating phases with a nontrivial
Z2 invariant and time-reversal symmetry protected gapless edge modes. We investigate the stability of these phases with respect to various symmetry-breaking perturbations and demonstrate the connection to the recent discovery of an exactly solvable
S=1/2 chiral spin-liquid model [Yao and Kivelson, Phys. Rev. Lett. 99, 247203 (2007)] with non-Abelian and Abelian excitations on the same lattice at strong interaction strength. Our work highlights the relationship between noninteracting topological band insulators and strongly interacting topologically ordered spin systems, and points to promising avenues for enlarging the number of known examples of both.