Extended Bose-Hubbard model on a honeycomb lattice

We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large-scale quantum Monte Carlo simulations. We present the ground-state phase diagrams for both the hard-core and the soft-core bosons. For the hard-core case, the transition between the ρ=1∕2 solid and the superfluid is first order, and the supersolid state is unstable toward phase separation. For the soft-core case, due to the presence of multiple occupation, a stable particle-induced supersolid (SS-p) phase emerges when 1∕2<ρ<1. The transition from the solid at ρ=1∕2 to the SS-p phase is second order with the superfluid density scaling as ρ_s∼ρ−1∕2. The SS-p phase has the same diagonal order as the solid at ρ=1∕2. As the chemical potential increases further, the SS-p phase turns into a solid where two bosons occupy each site of one sublattice through a first-order transition. We also calculate the critical exponents of the transition between the ρ=1∕2 solid and superfluid at the Heisenberg point for the hard-core case. We find the dynamical critical exponent z=0.15, which is smaller than results obtained on smaller lattices. This indicates that z approaches zero in the thermodynamic limit, and thus the transition is also first order even at the Heisenberg point.