The Extended Bose Hubbard Model on the Two Dimensional Honeycomb Lattice

Details The Extended Bose Hubbard Model on the Two Dimensional Honeycomb Lattice The Extended Bose Hubbard Model on the Two Dimensional Honeycomb Lattice

2007-01-06

arxiv.org/abs/cond-mat/0701120v2

Phys. Rev. B 75, 214509 (2007).

Physics

Condensed Matter

Other Condensed Matter

6pages, 6figures

Scientific paper

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.

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