Quantum phase transitions studied within the interacting boson model

We study quasicritical phenomena in transitions between two "quantum phases" of a finite boson system, described by the interacting boson model 1 used in nuclear physics. The model is formulated in the algebraic framework and has a simple geometrical interpretation; the "phases" represented by dynamical symmetries U(5) and SU(3) correspond to spherical and deformed nuclear shapes. The quasicriticality of the U(5)-SU(3) transition is shown to be connected with the following phenomena simultaneously occurring in a narrow parameter region between the symmetries: (a) abrupt structural changes of eigenstates, (b) multiple avoided crossing of levels, (c) peaked density of exceptional points, (d) qualitative changes of the corresponding classical potential. We show that these spectroscopic features influence the dynamics of intersymmetry transitions in the model parameter space if the parameters themselves become dynamical variables.