Anharmonicity effects in the bosonic U(2)-SO(3) excited-state quantum phase transition

We study the effect of the inclusion of the U(2) Lie algebra second-order Casimir operator in a model Hamiltonian of the vibron model two-dimensional limit. We extend previously published results, showing that the inclusion of the additional term does not alter the ground-state quantum phase transition between the symmetric and deformed limits of the model. Nevertheless, the inclusion of this operator implies deep changes on the excitation spectrum and on the ensuing excited-state quantum phase transitions.