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Detailed Analysis of Quantum Phase Transitions Within the u(2) Algebra

We analyze in detail the quantum phase transitions that arise in models based on the u(2) algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians that admix the two dynamical symmetry chains u(2)⊃ u(1) and u(2) ⊃so(2) by diagonalizing the problem exactly in the u(1) basis. Then we apply the coherent state formalism to determine the energy functional. Finally we show that a quantum phase transition of a different nature, but displaying similar characteristics, may arise also within a single chain just by including higher order terms in the hamiltonian.