Phase diagram and multicritical behaviors of mixtures of 3D bosonic gases

We investigate the Bose-Einstein condensation patterns, the critical and multicritical behaviors of three-dimensional mixtures of bosonic gases with short-range density-density interactions. These systems have a global U(1)+U(1) symmetry, as the system Hamiltonian is invariant under independent U(1) transformations acting on each species. In particular, we consider the three-dimensional Bose-Hubbard model for two lattice bosonic gases coupled by an on-site inter-species density-density interaction. We study the phase diagram and the critical behaviors along the transition lines characterized by the Bose-Einstein condensation of one or both species. We present mean-field calculations and numerical finite-size scaling analyses of quantum Monte Carlo data. We also consider multicritical points, close to which it is possible to observe the condensation of both gas components. We determine the possible multicritical behaviors by using field-theoretical perturbative methods. We consider the U(1)+U(1)-symmetric Landau-Ginzburg-Wilson Phi4 theory and determine the corresponding stable fixed points of the renormalization-group flow. The analysis predicts that, in all cases, the multicritical behavior is analogous to the one that would be observed in systems of two identical gases, with an additional Z_2 exchange symmetry.