The studies of ultracold dipolar bosons have
been stimulated by the creation of Bose-Einstein condensates of 52Cr ,
164Dy , and 168Er  with strong magnetic dipole-dipole interactions
and gases of polar molecules . In this work, we consider dipolar
hardcore bosons in two-dimensional optical lattices and assume that the
dipole moments are polarized to the direction perpendicular to the
lattice plane, i.e., the interaction is isotropic. We focus on the two
different types of lattice, namely a square lattice and a triangular
In the former case, we investigate the
stability of superflow in a moving optical lattice using the linear
spin-wave theory . It has been predicted in previous work that there
are stable supersolid (SS) phases, which possess both superfluid (SF) and
crystalline orders, in dipolar hardcore bosons in a square lattice. We
show that the critical velocities for the SS phases are significantly
smaller than that for the SF phase. We also find that increasing the
superflow can induce the phase transition from a SF to a checkerboard SS.
We confirm that such a flow-induced SF-SS transition can indeed occurs
during the dipole oscillation in the presence of a trapping potential .
In a triangular lattice, we discuss
quantum phase transitions between SF, SS, and Neel solid . We find
that the SF-SS transition is of the first order, in contrast with
previous quantum Monte Carlo
simulations. We show that the SF-SS (or solid) transition can exhibit an
anomalous hysteresis, in which a standard loop structure is not formed. It
is found that the transition occurs unidirectionally as a consequence of
the anomalous hysteresis.
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