Study of Long-Range Orders Due to Cooperative Breathing Mode in Two Dimensions

We study hard-core-bosons (HCBs) on a square lattice with a perovskite-type structure. The HCBs interact with the in-plane (xy) oxygen atoms via cooperative breathing mode. On the other hand, non-cooperative HCB-phonon interaction exists for the out-of-plane oxygen atoms in the z-direction. Using a non-perturbative treatment, we derive an effective Hamiltonian which involves nearest-neighbor, next-nearest-neighbor and next-to-next-nearest-neighbor hoppings and repulsions. Using a quantum Monte Carlo simulation involving stochastic-series-expansion method, we construct the phase diagram of the system. At half-filling, the system exhibits a checkerboard solid characterized by ordering wavevector $\vec{Q}=(\pi,\pi)$. Slightly away from half-filling, we get a region of checkerboard supersolid, the width of which decreases with increasing HCB-phonon interaction strength. On the other hand at $\frac{1}{3}$-filling, the system manifests the existence of a novel striped solid with a peak in the structure factor at wavevector $\vec{Q}=(2\pi/3,2\pi/3)$ or $(2\pi/3,4\pi/3)$. On both sides of this charge-density-wave, we get a striped supersolid with an asymmetry in the extent.