Phase diagram and multicritical behaviors of mixtures of three-dimensional bosonic gases

We investigate the Bose-Einstein condensation (BEC) patterns, the critical and multicritical behaviors of three-dimensional mixtures of bosonic gases with density-density interactions, characterized by a global U(1)⊕U(1) symmetry [one U(1) transformation for each species]. In particular, we consider the three-dimensional Bose-Hubbard model for two lattice bosonic gases coupled by an on-site interspecies density-density interaction. We study the phase diagram and the critical behaviors along the transition lines of the BEC of one or both species. We present mean-field calculations and finite-size scaling analyses of quantum Monte Carlo data. We also investigate the nature of the multicritical points where the BEC transition lines of the two species meet. The corresponding universality classes are inferred from a renormalization-group analysis of the corresponding multicritical U(1)⊕U(1) Landau-Ginzburg-Wilson Φ4 theory. We find two distinct critical behaviors, associated with bicritical and tetracritical points, respectively, depending on the relative strength of the interspecies and intraspecies interactions