π-Phase shift in a two-dimensional hardcore Bose-Hubbard model with imposed stripes

π-phase shift is crucial in strongly-correlated systems and plays a significant role in understanding the Hubbard model, which provides insights into the electronic structures and superconducting properties of the cuprate materials. In this paper, we present a comprehensive study to investigate the intriguing π-phase shift in the striped Bose-Hubbard model in a two-dimensional square lattice, as an extension of phenomena observed in the Hubbard model. The stochastic Green's function method is employed to investigate the model. By introducing stripes with higher potential energy, measurements of the density-density correlations reveal a distinct π-phase, where sublattices with higher and lower densities are reversed across the imposed stripes.