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.
Signatures of criticality in the evolution of the nuclear ground-state shapes across the $N\ifmmode\times\else\texttimes\fi{}Z$ plane are discussed. Attention is paid to specific data indicating sudden structural changes in various isotopic and isotonic chains of medium-mass and heavy even-even nuclei, as well as to diverse theoretical aspects of the models used to describe these changes. The interacting boson model and the geometric collective model, in particular, are discussed in detail, the former providing global predictions for the evolution of collective observables in nuclei between closed shells and the latter yielding a parameter-efficient description of nuclei at the critical points of shape transitions. Some issues related to the mechanism of first- and second-order quantum phase transitions in general many-body systems are also outlined.
Abstract. The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods. We have extended the SMMC method to heavy nuclei and used it to study the transition from vibrational (spherical) to rotational (deformed) nuclei in families of rare-earth isotopes. We have calculated collective enhancement factors of level densities as a function of excitation energy and found that the decay of the vibrational and rotational enhancements is well correlated with the pairing and shape phase transitions, respectively.
We investigate the role of the permutationally invariant part of the density matrix (PIDM) in capturing the properties of the ground state of the system during a quantum phase transition. In the context of quantum state tomography, PIDM is known to be obtainable with only a low number of measurement settings, namely
O(L2), where
L is the system size. Considering the transverse-field Ising chain and the
XXZ chain as examples, we compute the second-order R\'enyi entropy of PIDM for the ground state by using the density-matrix renormalization-group algorithm. In the transverse-field Ising chain with ferromagnetic interaction, the ground state is permutationally invariant both in the limits of zero and infinite field, leading to a vanishing R\'enyi entropy of PIDM. The latter exhibits a broad peak as a function of the transverse field around the quantum critical point, which gets more pronounced for larger system size. In the antiferromagnetic case, the peak structure disappears and the R\'enyi entropy diverges like
O(L) in the whole field range of the ordered phase. In the
XXZ model with ferromagnetic interaction, the ground state is permutationally invariant in the full parameter regime of easy-axis anisotropy, causing the R\'enyi entropy of PIDM to vanish. In the easy-plane region, the R\'enyi entropy of PIDM grows almost linearly as a function of the system size. In the antiferromagnetic case, the R\'enyi entropy of PIDM takes finite values at any point in parameter space; importantly, its minimum appears at the phase-transition point. We discuss the cause of these behaviors of the R\'enyi entropy of PIDM, examining the possible application of this experimentally tractable quantity to the analysis of phase-transition phenomena.
A study of first and second order nuclear shape phase transitional behavior in yrast states of even-even nuclei in the context of the Interacting Boson Model-1 is presented. Finite boson number effects are identified using calculations with up to 150 bosons, and the role of the rotational degree of freedom of observables in first and second order quantum phase transitional nuclei is discussed. We aim to provide a first investigation of the angular momentum dependence of experimentally accessible phase transitional signatures in finite-sized quantum nuclear systems.