Scalar two-level boson model to study the interacting boson model phase diagram in the Casten triangle

Abstract

We introduce a simple two-level boson model with the same energy surface as the Q-consistent interacting boson model Hamiltonian. The model can be diagonalized for large number of bosons and the results used to check analytical finite-size corrections to the energy gap and the order parameter in the critical region.

Concurrence in collective models

“…where x c = (4+y 2 )/(5+y 2 ) is known to be the transition point [36]. The correspondence with the uniaxial model Hamiltonian (36) is then straighforward.…”

“…The main advantage of the parametrization (A1), in terms of the two bosons s and t, is that the order parameter is simply n t /N [36].…”

“…Within the parametrization (36), it is not easy to build an order parameter characterizing this transition. However, in the Appendix, we give the correspondence between this model and a two-level boson problem recently introduced in nuclear physics [36] which allows one to get an order parameter. For h z > 1, a simple mean-field analysis similar to those presented in Ref.…”

“…VI. In the Appendix, we establish the correspondence between the uniaxial model in an arbitrary field and a two-level boson model recently proposed in nuclear physics [36] which allows a simple physical interpretation of the order parameter.…”

Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

“…The interacting boson model (IBM) was introduced by Arima and Iachello to describe the structure of low energy states of even-even medium and heavy nuclei [50]. For the sake of simplicity, we use the IBM-LMG, a simplified version of the model built with scalar bosons [51]. Finally, the vibron model was also proposed by Iachello to describe the rovibrational structure of molecules [52] and the 2DVM was introduced [53] to model molecular bending dynamics (e.g., see Ref.…”