Correlated phases of bosons in the at lowest band of the dice lattice

The many-body physics of particles on lattices subject to a gauge field can lead to phases resembling fractional quantum Hall liquids [1]. Here, we study correlated phases occurring in the lowest band of the dice lattice model at flux density one half, which is perfectly flat. In addition, we show that this model has a clean realisation in cold atomic gases, using an optical lattice based on an anti-magic wavelength for trapping Yb atoms in their ground state and first excited state at minima and maxima of the optical intensity, respectively. This model yields an example of a time-reversal symmetric Hamiltonian with topologically trivial bands, so our results can be seen in contrast to the fractional Chern insulators which occur in bands with non-zero Berry curvature. We construct the projection of the model to the lowest dice band that yields an effective model on a triangular lattice which is described by a Hubbard-Hamiltonian with interaction-assisted hopping processes. We solve this model for bosons in two limits [2]. In the limit of large density, we use Gross-Pitaevskii mean-field theory to reveal time-reversal symmetry breaking vortex lattices phases, which can be mapped onto the highly degenerate groundstate manifold of the --model on the dice lattice. At low density, we use exact diagonalization to identify three stable phases of the effective model, which are found at fractional filling factors of the lowest band, including a classical crystal at , a supersolid state at , and a Mott insulator at . [1] G. Möller and N. R. Cooper, Phys. Rev. Lett. 103, 105303 (2009). [2] G. Möller and N. R. Cooper, Phys. Rev. Lett. 108, 045306 (2012).