Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

Abstract

The spectral characteristics of the L π = 0 + excited-states in the interacting boson model are systematically investigated. It is found that various types of excited-state quantum phase transitions may widely occur in the model as functions of the excitation energy, which indicates that the phase diagram of the interacting boson model can be dynamically extended along the direction of the excitation energy. It has also been justified that the d-boson occupation probability ρ(E) is qualified to be taken as the effective order parameter to identify these excited-state quantum phase transitions. In addition, the underlying relation between the excite-state quantum phase transition and the chaotic dynamics is also stated.

Jacobi-type transitions in the interacting boson model

“…2(a), where the γ-soft picture appearing outside of the well is due to the U(5) DS involved in the Hamiltonian. This transition from SU(3) to U(5) can be regarded as an extension of the U(5)-SU(3) GSQPT along the excitation energy [13]. As seen in Fig.…”

“…However, because of the Z 2 symmetry, χ → −χ, of the potential energy surface (2), we confine our discussion here to χ ≤ 0. It has been shown [6,9,13] that associated with GSQPTs of Fig. 1, there are, in the deformed region of the phase diagram, ESQPTs.…”

“…Considerable attention has very recently been given to the so-called excited state QPT (ESQPT) [5][6][7][8][9][10][11][12][13]. Unlike GSQPT, an ESQPT can occur not only with variation of the control parameters of a model Hamiltonian, but also with increasing excitation energy.…”

“…Evidence of the ESQPT associated with the GSQPT in the VM [9,10] have been identified from the bending motions in non-rigid molecules [16,17]. However, there is still no experimental evidence reported for ESQPT in nuclei despite the fact that model calculations within the IBM have shown that more abundant ESQPTs are present in the large-N limit of this model [13].…”

“…The critical excitation energy, E c , varies from zero along the critical value, η = η c , to the top of the spectrum of η = 1. While a classification of the GSQPTs is feasible by means of the method of coherent states discussed above, a more complicated semi-classical analysis is needed in order to classify the associated ESQPTs [6,7,[11][12][13]25]. In the following, we will focus on (i) identification of signatures of ESQPTs associated with deformed nuclei rather than classification of ESQPTs in the IBM, and on (ii) whether or not ESQPTs or their precursors persist for finite N. We will also discuss whether the transitions are phase transitions or simply crossovers.…”