Degeneracy Of Energy Levels In The Phase Transitional Region Of The Interacting Boson Model

A schematic Hamiltonian of the interacting boson model has been used to study the phasetransition and the associated level degeneracy. Explicitly, the quantum phase transitionalbehaviors in large boson number have been analyzed, and the level degenercies occurringaround the critical point of the U(5)-SU(3) transition has been also checked in large bosonnumber. It is confirmed that this type of degeneracy can be well preserved in the first-orderphase transitional region. Moreover, a new type of level degeneracies has been identifiedaround the critical point of the U(5)-O(6) transition. Finally, the dynamical origin of the twotypes of level degenerations has been discussed. All the numerical calculations have beencarried within the IBAR program, which can be used to deal with the large-N calculations ofvarious quantities in the interacting boson model.