Study of supersolidity in the two-dimensional Hubbard-Holstein model

We derive an effective Hamiltonian for the two-dimensional Hubbard-Holstein model in the regimes of strong electron-electron and strong electron-phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a t(1) - V-1 - V-2 - V-3 Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling 1/8, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector (Q)over-right-arrow = (pi/4, 3 pi/4) or (pi/4, 5 pi/4). Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling 1/8 and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.