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

Abstract

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.

Spectral fluctuations in the interacting boson model*

“…To have a close look at the energy dependence of the P (S) and ∆ 3 (L) statistics, we select the cases at three different energy cutoffs from the panels (c2) and (c4) of It is given by ω = 0.25 (q = 0.45) for the spectrum below E/N = 0.19 but by ω = 0.79 (q = 0.92) for that above E/N = 0.19. Since E/N = 0.19 is very close to the critical energy E lmin , the results confirm again that the spectral fluctuations could be significantly different by taking the stationary point V lmin as a boundary as did in [29]. In short, the spectral fluctuations in the deformed phase of the U(5)-SU(3) GSQPT are shown to be more energy dependent due to the richer stationary point structure.…”

“…In the analysis given in [29], the stationary points V lmax and V lmin were taken as the phase boundaries to do the statistical analysis of the excited state quantum phase transitions (ESQPTs). Clearly, the present results further justify the reasonability of doing so.…”

“…It means that the excited states in an IBM system can be divided into different "families" according to the stationary points [28]. The recent analysis [29] has revealed that the spectral fluctuations in the different "families" are indeed different especially in the chaotic region of the IBM. Such a finding was gained from the statistical calculations by predividing the excited states into different groups based on the mean-field analysis [29].…”

“…The recent analysis [29] has revealed that the spectral fluctuations in the different "families" are indeed different especially in the chaotic region of the IBM. Such a finding was gained from the statistical calculations by predividing the excited states into different groups based on the mean-field analysis [29]. It is remained to answer whether or not the statistical results themselves can be taken as a criterion of distinguishing the excited states.…”

“…However, the spectral properties in a system may change as a function of the excitation energy. In particular, the excited state quantum phase transitions [23][24][25][26][27][28] were observed to widely occur in the IBM and suggested to be connected to the stationary points of the potential functions [23,24]. This means that the excited states in an IBM system can be divided into different "families" according to the stationary points [28].…”