Quantum phases of multiorbital bosonic gases in a hexagonal lattice

Orbital degree of freedom plays an important role for understanding quantum many-body phenomena. In this paper, we study an experimentally related setup with ultracold bosons loaded into hybridized bands of two-dimensional hexagonal optical lattices. We find that the system supports various quantum many-body phases at zero temperature, including chiral superfluid and chiral Mott insulating phases by breaking time-reversal symmetry, and the time-reversal-even insulating phase, based on dynamical mean-field theory. In the deep insulating regime, the time-reversal-even phase arises from the interplay of effective Dzyaloshinskii-Moriya and Heisenberg exchange interactions. To relate to experimental situations, we make band-structure calculations to obtain the Hubbard parameters, and show that these orbital ordering phases persist also in the presence of next-nearest-neighbor hopping.