Bose-Einstein condensation and critical behavior of two-component bosonic gases

We study Bose-Einstein condensation (BEC) in three-dimensional two-component bosonic gases, character- izing the universal behaviors of the critical modes arising at the BEC transitions. For this purpose, we use field-theoretical (FT) renormalization-group (RG) methods and perform mean-field and numerical calculations. The FT RG analysis is based on the Landau-Ginzburg-Wilson ! 4 theory with two complex scalar fields which has the same symmetry as the bosonic system. In particular, for identical bosons with exchange Z2 symmetry, coupled by effective density-density interactions, the global symmetry is Z2,e ⊗ U(1) ⊗ U(1). At the BEC transition, it may break into Z2 ,e ⊗ Z2 ⊗ Z2 when both components condense simultaneously, or to U(1) ⊗ Z2 when only one component condenses. This implies different universality classes for the corresponding critical behaviors. Numerical simulations of the two-component Bose-Hubbard model in the hard-core limit support the RG prediction: when both components condense simultaneously, the critical behavior is controlled by a decoupled XY fixed point, with unusual slowly decaying scaling corrections arising from the onsite interspecies interaction.