Critical behavior of the supersolid transition in Bose-Hubbard models

We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF-CSS transition is in the three-dimensional XY universality class. The SF-XSS transition exhibits nontrivial critical behavior, and appears, within a d=3-epsilon expansion, to be driven generically first order by fluctuations. However, within a one-loop calculation directly in d=2 a strong-coupling fixed point with striking ''non-Bose-liquid'' behavior is found. At special isolated multicritical points of particle-hole symmetry, the system falls into the three-dimensional Ising universality class.