Statistical analysis of the excited-state quantum phase transitions in the interacting boson model

Wen Ting Dong, Liaoning Normal University
Yu Zhang, Liaoning Normal University
Bing Cheng He, Nankai University
Feng Pan, Liaoning Normal University
Yan An Luo, Nankai University
J. P. Draayer, Louisiana State University
S. Karampagia, Michigan State University


The spectral fluctuations and transition intensity fluctuations in the excited-state quantum phase transitions (ESQPTs) have been investigated within the framework of the interacting boson model (IBM) by adopting three statistical measures, including the nearest neighbor level spacing distribution P(S) measuring the chaoticity (regularity) in energy spectra, the Δ3(L) statistics of Dyson and Mehta measuring the spectral rigidity and the intensity distribution P(y) measuring the chaoticity (regularity) in B(E0) transitions. The results indicate that that the ESQPT as a function of the excitation energy may occur as a transition from regular (or semiregular) to highly chaotic if only the associated whole spectrum is chaotic, which fits most of the deformed situations in the IBM including those in the U(5)-SU(3) and SU(3)-O(6) transitional regions. Otherwise, the ESQPT will appear as a transition from regular (or semiregular) to regular such as the cases in the U(5)-O(6) transitional region or those on the 'Alhassid-Whelan arc', which represents a nearly regular parameter region connecting the U(5) and SU(3) limits in the IBM.