Quantum Phase Transition in Binary Ultra-cold Bose Gases

The quantum phase transition in binary Bose Gases is studied using the Cornwall-Jackiw-Tomboulis effective potential approach in the double-bubble approximation, which preserves the Goldstone theorem. Its main feature is that the transition is second order occurring at ultra-cold temperatures associated with the type of inverse symmetry-breaking transition occurring when the chemical potential reaches a critical value. However, it cannot simultaneously occur for the two components of a binary mixture of Bose gases.