Quantum field theory for the three-body constrained lattice Bose gas. II. Application to the many-body problem

We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a continuous supersolid, which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.