Frustration induced incommensurate solids in the extended Bose-Hubbard model

We study the extended Bose-Hubbard model with nearest-neighbor and next-nearest-neighbor $(V,V^{\mathrm{\prime }})$ repulsive interactions on a square lattice by using the quantum Monte Carlo method. Unlike the case of strong $V^{\mathrm{\prime }}$ where the ground states can be striped solids or striped supersolids, we focus on weak $V^{\mathrm{\prime }}<V\mathrm{/}2$ and small hoppings and find that, in the thermodynamic limit, incommensurate solids of fractional densities varying from 1/4 to 1/2 can be stabilized. We also show that the incommensurate solids, which are characterized by a continuous set of wave vectors changing from $(\pi ,\pi \mathrm{/}2)$ (or $(\pi \mathrm{/}2,\pi )$) to $(\pi ,\pi )$, can be understood by a mechanism of domain wall formation. The related ground-state phase diagram and thermal phase transitions are also discussed.