Emergent spectral degeneracies in the quantum phase transitions in the interacting boson model

Abstract

The spectral degeneracies emerging in the critical region of the interacting boson model are systematically investigated. The results indicate that the level crossings in the transitions from the U(5) to the SU(3) quasidynamical symmetry can induce the approximate spectral degeneracies along the first-order transitional line for large boson number $N$. The remnants of these types of degeneracies in finite-$N$ systems have been preliminarily identified from the low-lying spectra of $^{150}\mathrm{Nd}$. In addition, the similar approximate degeneracies emerging in the phase transition between the U(5) and SO(6) quasidynamical symmetries are parallel emphasized and those in other critical models are also mentioned.