A classical fluctuation theory of the superfluid, Mott, and normal phases of correlated bosons

We present a method that generalises the standard mean field theory of correlated lattice bosons to include amplitude and phase fluctuations of the U(1) field that induces onsite particle number mixing. We solve the resulting problem, initially, by using a classical approximation for the particle number mixing field and a Monte Carlo treatment of the resulting bosonic model. In two dimensions we obtain Tc scales that dramatically improve on mean field theory and are within about 20% of quantum Monte Carlo estimates at density n = 1. The ground state, however, is still mean field, with an overestimate of the critical interaction, Uc, for the superfluid to Mott transition. Further including gaussian quantum fluctuations strikingly improves the Uc and the overall thermal phase diagram. The approach has a computational cost that is linear in system size, readily generalises to multispecies bosons, disorder, and the presence of traps, and yields real frequency response functions