Topological Flat Bands from Dipolar Spin Systems
  We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultra-cold polar molecules or spins in the solid state is considered. 
Norman Y. Yao, Chris R. Laumann, Alexey V. Gorshkov, Steven D.   Bennett, Eugene Demler, Peter Zoller, Mikhail D. Lukin
cond-mat.str-el cond-mat.quant-gas quant-ph