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arXiv:nucl-th/0309004 · Physical Review Letters

Quantum Phase Transitions in the Interacting Boson Model: Integrability, Level Repulsion, and Level Crossing

J. M. Arias, J. Dukelsky, J. E. García-Ramos

Published Oct 14, 2003• 64 citations
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Abstract

We study the quantum phase transition mechanisms that arise in the interacting boson model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.

DOI
10.1103/physrevlett.91.162502

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We study the quantum phase transition mechanisms that arise in the interacting boson model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.
We investigate the evolution of quantal spectra and the corresponding wave functions along the [O(6)-U(5)] \ensuremath{\supset} O(5) transition of the interacting boson model. The model is integrable in this regime, and its ground state passes through a second-order structural phase transition. We show that the whole spectrum as a function of the Hamiltonian control parameter as well as structures of all excited states exhibit rather organized and correlated behaviors, which provide deeper insight into the nature of this transitional path.
The spectral degeneracies emerging in the critical region of the interacting boson model are systematically investigated. The results indicate that the level crossings in the transitions from the U(5) to the SU(3) quasidynamical symmetry can induce the approximate spectral degeneracies along the first-order transitional line for large boson number NNN. The remnants of these types of degeneracies in finite-NNN systems have been preliminarily identified from the low-lying spectra of 150Nd^{150}\mathrm{Nd}150Nd. In addition, the similar approximate degeneracies emerging in the phase transition between the U(5) and SO(6) quasidynamical symmetries are parallel emphasized and those in other critical models are also mentioned.
We study quasicritical phenomena in transitions between two "quantum phases" of a finite boson system, described by the interacting boson model 1 used in nuclear physics. The model is formulated in the algebraic framework and has a simple geometrical interpretation; the "phases" represented by dynamical symmetries U(5) and SU(3) correspond to spherical and deformed nuclear shapes. The quasicriticality of the U(5)-SU(3) transition is shown to be connected with the following phenomena simultaneously occurring in a narrow parameter region between the symmetries: (a) abrupt structural changes of eigenstates, (b) multiple avoided crossing of levels, (c) peaked density of exceptional points, (d) qualitative changes of the corresponding classical potential. We show that these spectroscopic features influence the dynamics of intersymmetry transitions in the model parameter space if the parameters themselves become dynamical variables.
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.
The U (5)– O (6) transitional behaviour of the interacting Boson model in the large- N limit is revisited. Some low-lying energy levels, overlaps of the ground state wavefunctions, B ( E 2) transition rate for the decay of the first excited energy level to the ground state, and the order parameters are calculated for different total numbers of bosons. The results show that critical behaviours of these quantities are greatly enhanced with an increase in the total number of bosons N ; in particular, the fractional occupation probability for d bosons in the ground state, the difference between the expectation value of n d in the first excited 0 + state and the ground state, and another quantity related to the isomer shift behave similarly in both the O (6)– U (5) large- N and U (5)– SU (3) phase transitions.