The Extended Bose Hubbard Model on the Two Dimensional Honeycomb Lattice

Abstract

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 case and the soft-core case. For the hard-core case, the transition between $\rho =1/2$ solid and the superfluid is first order and the supersolid state is unstable towards phase separation. For the soft-core case, due to the presence of the multiple occupation, a stable particle induced supersolid (SS-p) phase emerges when $1/2<\rho <1$. The transition from the solid at $\rho =1/2$ to the SS-p is second order with the superfluid density scaling as ${\rho }_s\sim \rho -1/2$. The SS-p has the same diagonal order as the solid at $\rho =1/2$. As the chemical potential increasing further, the SS-p will turn into a solid where two bosons occupying each site of a sublattice through a first order transition. We also calculate the critical exponents of the transition between $\rho =1/2$ 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, so the transition is also first order even at the Heisenberg point.

6pages, 6figures

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