Different quantum phases of a hard-core boson induced by dipole-dipole interaction with varying angles of polarization are discussed in this work. We consider the two most influential leading terms with anisotropy due to the tilted polarization of the on-site boson in the square lattice. To ensure the concreteness of this truncation, we compare our phase diagrams, obtained numerically from the cluster mean-field theory (CMFT) and infinite projected entangled-pair state (iPEPS), with that of the long-range interacting model from quantum Monte Carlo. Next, we focus on the case where the azimuthal angle is fixed to $\ensuremath{\phi}=\ensuremath{\pi}/4$. Using the mean-field analysis where the quantum spin operators are replaced by
c numbers, we aim to search for the underlying phases, especially the supersolid. Our results show a competing scenario mainly between two ordered phases with different sizes of unit cell, where a first-order transition takes place in between them. With the help of the CMFT and variational iPEPS, the phase boundaries predicted by the mean-field theory are determined more precisely. Our discoveries elucidate the possible underlying supersolid phases which might be seen in the ultracold experiments with strongly dipolar atoms. Moreover, our results indicate that an effective triangular optical lattice can be realized by fine tuning the polarization of dipoles in a square lattice.
We study ground state properties and excitation spectra for hard-core bosons on square and triangular lattices, at half filling, using series expansion methods. Nearest-neighbor repulsion between the bosons leads to the development of short-range density order at the antiferromagnetic wave vector, and simultaneously, a minimum in the density excitation spectra. On the square lattice, the model maps onto the well studied
XXZ model, and the gap at the minimum collapses to zero precisely at the Heisenberg symmetry point, leading to the well known spectra for the Heisenberg antiferromagnet. On the triangular lattice, the collapse of the gap at the minimum signals the onset of the supersolid phase. Our results suggest that the transition from the superfluid to the supersolid phase may be weakly first order. We also find several features in the density of states, including two peaks and a sharp discontinuity, which may be observable in experimental realization of such systems.
We study ground state properties and excitation spectra for hard-core Bosons on square and triangular lattices, at half filling, using series expansion methods. Nearest-neighbor repulsion between the Bosons leads to the development of short-range density order at the antiferromagnetic wavevector, and simultaneously a roton minima in the density excitation spectra. On the square-lattice, the model maps on to the well studied XXZ model, and the roton gap collapses to zero precisely at the Heisenberg symmetry point, leading to the well known spectra for the Heisenberg antiferromagnet. On the triangular-lattice, the collapse of the roton gap signals the onset of the supersolid phase. Our results suggest that the transition from the superfluid to the supersolid phase maybe weakly first order. We also find several features in the density of states, including two-peaks and a sharp discontinuity, which maybe observable in experimental realization of such systems.