Effect of Harmonic potential in Anisotropic Dipolar Lattice Bosons

Recent progress in realizing quantum degenerate dipolar gases in optical lattices has opened new avenues for studying quantum systems with anisotropic, long-range interactions. In this work, we investigate the zero-temperature phase diagram of hard-core dipolar bosons at half-filling confined in a two-dimensional square optical lattice. The dipoles are aligned parallel to each other and tilted out of the lattice plane by an external electric field, with the azimuthal angle fixed angle of 45 degree. Our results show that at zero temperature, the system remains superfluid (SF) for all tilt angles as long as the dipolar interaction strength remains below a critical valueV_c​. When the interaction strength exceeds this threshold, the SF phase becomes unstable and transitions into ordered phases such as checkerboard solids, diagonal stripe solids, or incompressible insulating states, depending on the tilt angle. We also find that the presence of a harmonic trap significantly influences these transitions by modifying the effective local interactions, enabling the coexistence of multiple competing phases. This study provides theoretical insight into the interplay between dipolar anisotropy, geometry, and external confinement, guiding future experimental efforts to realize and control exotic dipolar quantum matter in optical lattices.