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Journal of Physics A Mathematical and General

Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei

Pavel Cejnar, Michal Macek, Stefan G. Heinze, Jan Jolie, Jan Dobeš

Published Jul 19, 2006• 130 citations
Publisher

Abstract

Quantum phase transitions affecting the structure of ground and excited states of integrable systems with the Mexican-hat type potential are shown to be related to a singular torus of classical orbits passing the point of unstable equilibrium. As a specific example, we consider nuclear collective vibrations described by the O(6)–U(5) transitional Hamiltonian of the interacting boson model. While all states with zero values of the O(5) invariant undergo a continuous phase transition when crossing the energy of unstable equilibrium, the other states evolve in an analytic way.

DOI
10.1088/0305-4470/39/31/l01

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Quantum phase transitions affecting the structure of ground and excited states of integrable systems with the Mexican-hat type potential are shown to be related to a singular torus of classical orbits passing the point of unstable equilibrium. As a specific example, we consider nuclear collective vibrations described by the O(6)–U(5) transitional Hamiltonian of the interacting boson model. While all states with zero values of the O(5) invariant undergo a continuous phase transition when crossing the energy of unstable equilibrium, the other states evolve in an analytic way.
The series of articles [Ann. Phys. 345, 73 (2014) and Ann. Phys. 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with f=2f=2f=2 degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly many-body system. The intrinsic Hamiltonian formalism with angular momentum fixed to L=0L=0L=0 is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a nontrivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The features studied here are inherent in a great majority of interacting boson systems.
Structural evolutions in the U(5)-O(6) quantum phase transition are investigated within the framework of the interacting boson model by comparing the two types of effective order parameters in the ground-state quantum phase transition and excited-state quantum phase transition. It is found that the monopole-pair transfer intensities can show critical behaviors not only in the ground-state quantum phase transition but also in the excited-state quantum phase transition. It is thus suggested that the main features of the ESQPT should persist in nuclear systems.
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.