The Extended Bose Hubbard Model on the Two Dimensional Honeycomb Lattice

TL;DR

This paper investigates the phase diagram of the extended Bose-Hubbard model on a 2D honeycomb lattice using quantum Monte Carlo simulations, revealing phase transitions and the emergence of a stable supersolid phase.

Contribution

It provides the first detailed phase diagrams for both hard-core and soft-core cases, identifying the nature of phase transitions and the stability of supersolid phases in this model.

Findings

First-order transition between solid and superfluid at half-filling in the hard-core case.

Emergence of a stable particle-induced supersolid phase in the soft-core case.

Critical exponent analysis indicating a first-order transition at the Heisenberg point.

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.