E. Frey et L. Balents, CRITICAL-BEHAVIOR OF THE SUPERSOLID TRANSITION IN BOSE-HUBBARD MODELS, Physical review. B, Condensed matter, 55(2), 1997, pp. 1050-1067
We study the phase transitions of interacting bosons at zero temperatu
re 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 ari
sing in two dimensions on a square lattice. We find that the SF-CSS tr
ansition 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 fluc
tuations. However, within a one-loop calculation directly in d=2 a str
ong-coupling fixed point with striking ''non-Bose-liquid'' behavior is
found. At special isolated multicritical points of particle-hole symm
etry, the system falls into the three-dimensional Ising universality c
lass.