Flat Bands and Wigner Crystallization in the Honeycomb Optical Lattice

We study the ground states of cold atoms in the tight-binding bands built from p orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=(1/6) with a √(3)x√(3) structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at n=(1/2). Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments