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Physics of Atomic Nuclei

Studies of phase transitions and quantum chaos relationships in extended Casten triangle of IBM-1

J. Proskurins, A. Andrejevs, Tamara Krasta, J. J. Tambergs

Published Jul 1, 2006• 4 citations
Publisher

Abstract

A precise solution of the classical energy functional E(N, η, χ; β) minimum problem with respect to deformation parameter β is obtained for the simplified Casten version of the standard interacting boson model (IBM-1) Hamiltonian. The first-order phase transition lines as well as the critical points of X (5), -X (5), and E (5) symmetries are considered. The dynamical criteria of quantum chaos—the basis state fragmentation width and the wave function entropy—are studied for the ( η, χ ) parameter space of the extended Casten triangle, and the possible relationships between these criteria and phase transition lines are discussed.

DOI
10.1134/s1063778806070246

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A precise solution of the classical energy functional E(N, η, χ; β) minimum problem with respect to deformation parameter β is obtained for the simplified Casten version of the standard interacting boson model (IBM-1) Hamiltonian. The first-order phase transition lines as well as the critical points of X (5), -X (5), and E (5) symmetries are considered. The dynamical criteria of quantum chaos—the basis state fragmentation width and the wave function entropy—are studied for the ( η, χ ) parameter space of the extended Casten triangle, and the possible relationships between these criteria and phase transition lines are discussed.
The degree of chaos in the simplest interacting boson model (IBM-1) is compared with what we call the ``dynamical symmetry content'' of the system. The latter is represented by the information entropy of the eigenfunctions with respect to bases associated with dynamical symmetries of the IBM-1, and expresses thus the localization of actual eigenfunctions in these symmetry bases. The wave-function entropy is shown to be a sensitive tool for monitoring the processes of a single dynamical symmetry breaking or transitions between two and more symmetries. For the IBM-1 Hamiltonians studied here, the known features related to chaos, namely, the dependence of chaotic measures on the Hamiltonian parameters (position in the Casten triangle) and on the angular momentum, turn out to be correlated with the behavior of the wave-function entropy.
In this research, the quantum phase transition (QPT) in the Casten pyramid has been investigated using entanglement entropy. Energy surfaces and the entanglement entropy have been obtained within the framework of semi-classical approximation interacting boson model-2 (IBM-2) using Schmidt decomposition and coherent states formalism. The results showed that the entanglement entropy is a suitable and efficient tool for investigating QPT and determining critical points in the connected pathes to the Uπν(5){U_{\pi \nu }}\left( 5\right)Uπν​(5) limit, and pathes of SUπν(3)↔Oπν(6)↔SUπν(3)‾S{U_{\pi \nu }}\left( 3 \right) \leftrightarrow {O_{\pi \nu }}\left( 6 \right) \leftrightarrow \overline{S{U_{\pi \nu }}\left( 3 \right) }SUπν​(3)↔Oπν​(6)↔SUπν​(3)​ and SUπν∗(3)↔Oπν(6)↔SUπν∗(3)‾SU_{\pi \nu }^*\left( 3 \right) \leftrightarrow {O_{\pi \nu }}\left( 6 \right) \leftrightarrow \overline{SU_{\pi \nu }^*\left( 3 \right) }SUπν∗​(3)↔Oπν​(6)↔SUπν∗​(3)​ . The description of QPT using numerical analysis of energy surfaces confirms the results of entanglement entropy.
The evolution of system observables at critical points of quantum phase transitions in atomic nuclei is explored within the context of the interacting boson model-1. The evolution of energies and transition strengths in the ground state band at the infinite-size critical point are examined with respect to system size. Properties of first-order phase transitions away from the U(5)-SU(3) leg of the Casten triangle are examined, and the effects of angular momentum on the evolution of system observables at the critical point are investigated for the first time.
Quantum phase transitional patterns in the whole parameter space of the consistent-Q Hamiltonian in the Interacting Boson Model are studied based on an implemented Fortran code for numerical computation of the matrix elements in the SU (3) Draayer-Akiyama basis. Results with respect to both ground and some excited states of the model Hamiltonian are discussed. Quantum phase transitional behavior under a variety of parameter situations is shown. It is found that transitional behavior of excited states is more complicated. Pt isotopes are taken as examples in illustrating the prolate-oblate shape phase transition.
Properties of quantum phase transitional systems in atomic nuclei are explored within the context of the interacting boson model 1 for both first and second order systems. A traditionally experimental approach is used to search for the effective finite-size critical point as a function of system size and angular momentum by studying derivatives of observables across the phase transition region. The effects of angular momentum on quantum phase transitions are investigated, and properties of first order phase transitions within the Casten triangle are examined.
The phase diagram of two-level boson Hamiltonians, including the interacting boson model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.