|   The studies of ultracold dipolar bosons have
      been stimulated by the creation of Bose-Einstein condensates of 52Cr [1],
      164Dy [2], and 168Er [3] with strong magnetic dipole-dipole interactions
      and gases of polar molecules [4]. 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
      lattice.In the former case, we investigate the
      stability of superflow in a moving optical lattice using the linear
      spin-wave theory [5]. 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 [6].
 In a triangular lattice, we discuss
      quantum phase transitions between SF, SS, and Neel solid [7]. 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.
 
 References:
 [1] A. Griesmaier et al., Phys. Rev. Lett.
      94, 160401 (2005).
 [2] M. Lu et al., Phys. Rev. Lett. 107,
      190401 (2011).
 [3] K. Aikawa et al., Phys. Rev. Lett 108,
      210401 (2012).
 [4] K. Aikawa et al., Phys. Rev. Lett. 105,
      203001 (2010).
 [5] I.
      Danshita and D. Yamamoto, Phys. Rev. A 82, 013645 (2010).
 [6] T. Saito, I.
      Danshita, T. Ozaki, and T. Nikuni, Phys. Rev. A 86,
      023623 (2012).
 [7] D. Yamamoto, I. Danshita, and C. A. R.
      Sa de Melo, Phys. Rev. A 85, 021601
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