The spectral characteristics of the ${L}^{\ensuremath{\pi}}={0}^{+}$ 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 $\ensuremath{\rho}(E)$ 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.
Abstract In this work, the von Neumann entropy has been calculated and employed as a probe to analyse quantum phase transitions (QPTs) within the -Interacting Boson Model ( -IBM). The von Neumann entropy between the -boson and -boson sectors is used as an indicator of QPTs and as a robust observable for the theoretical analysis of the isotopes. The von Neumann entropy correctly characterises the QPT in the transition region. The numerical results show that the and isotopes are located in the and limits, respectively.
Background: One of the fundamental problems of quantum information science is quantum entanglement. Recently, quantum phase transition in nuclear systems is studied in connection with quantum entanglement.Purpose: In this paper, the use of entanglement entropy as a suitable signal for the study of quantum phase transition in the even-even and odd-
A nuclei is investigated. The effect of the coupling of a single fermion to a boson core on entanglement entropy is studied.Method: By use of the affine
SU(1,1) Lie algebra and through the Schmidt decomposition in the framework of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), entanglement entropy in the even-even and odd-
A are obtained. The entanglement entropy is used for tracking and studying the shape phase transition in these nuclei.Results: The entanglement entropy in the IBM and the IBFM is calculated. The entanglement entropy values of the low-lying states of
122−−134Xe,102−−110Pd, and
123−−133Xe were calculated and analyzed. It is found that entanglement entropy is a suitable order parameter to detect shape phase transition in nuclear systems.Conclusions: The obtained results indicate that the entropy of entanglement is sensitive to the shape-phase transition between spherical and $\ensuremath{\gamma}$-unstable regions in nuclei. The results show that entanglement entropy is a powerful tool for identifying shape phase transitions in nuclei. It is found that the coupling of the single fermion with angular momentum
j to the even-even system does not change the geometry imposed by the boson core performing the transition and only the entanglement entropy values have been shifted by the addition of the odd particle with respect to the even case.