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We investigate the Bose-Einstein condensation patterns, the critical andmulticritical behaviors of three-dimensional mixtures of bosonic gases withshort-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 thethree-dimensional Bose-Hubbard model for two lattice bosonic gases coupled byan on-site inter-species density-density interaction. We study the phasediagram and the critical behaviors along the transition lines characterized bythe Bose-Einstein condensation of one or both species. We present mean-fieldcalculations and numerical finite-size scaling analyses of quantum Monte Carlodata. We also consider multicritical points, close to which it is possible toobserve the condensation of both gas components. We determine the possiblemulticritical behaviors by using field-theoretical perturbative methods. Weconsider the U(1)+U(1)-symmetric Landau-Ginzburg-Wilson Phi4 theory anddetermine the corresponding stable fixed points of the renormalization-groupflow. The analysis predicts that, in all cases, the multicritical behavior isanalogous to the one that would be observed in systems of two identical gases,with an additional Z_2 exchange symmetry.

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