Phase Structure of the Interacting Vector Boson Model

The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a dynamical group possesses a rich algebraic structure of physical interesting subgroups that define its distinct exactly solvable dynamical limits. The classical images corresponding to different dynamical symmetries are obtained by means of the coherent state method. The phase structure of the IVBM is investigated and the following basic phase shapes, connected to a specific geometric configurations of the ground state, are determined: spherical, $U_{p}(3)\otimes U_{n}(3)$, $\gamma-$unstable, O(6), and axially deformed shape, $SU(3)\otimes U_{T}(2)$. The ground state quantum phase transitions between different phase shapes, corresponding to the different dynamical symmetries and mixed symmetry case, are investigated.