Quantum phase transitions in the interacting boson model

Abstract

This review is focused on various properties of quantum phase transitions (QPTs) in the Interacting Boson Model (IBM) of nuclear structure. The model in its infinite-size limit exhibits shape-phase transitions between spherical, deformed prolate, and deformed oblate forms of the ground state. Finite-size precursors of such behavior are verified by robust variations of nuclear properties (nuclear masses, excitation energies, transition probabilities for low lying levels) across the chart of nuclides. Simultaneously, the model serves as a theoretical laboratory for studying diverse general features of QPTs in interacting many-body systems, which differ in many respects from lattice models of solid-state physics. We outline the most important fields of the present interest: (a) The coexistence of first- and second-order phase transitions supports studies related to the microscopic origin of the QPT phenomena. (b) The competing quantum phases are characterized by specific dynamical symmetries and novel symmetry related approaches are developed to describe also the transitional dynamical domains. (c) In some parameter regions, the QPT-like behavior can be ascribed also to individual excited states, which is linked to the thermodynamic and classical descriptions of the system. (d) The model and its phase structure can be extended in many directions: by separating proton and neutron excitations, considering odd-fermion degrees of freedom or different particle-hole configurations, by including other types of bosons, higher order interactions, and by imposing external rotation. All these aspects of IBM phase transitions are relevant in the interpretation of experimental data and important for a fundamental understanding of the QPT phenomenon.

a review article, 71 pages, 18 figures

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• Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
• Nuclear quantum shape-phase transitions in odd-mass systems
• Quartic oscillator potential in the γ-rigid regime of the collective geometrical model
• The subtle connection between shape coexistence and quantum phase transition. The Zr case
• Probing the excited-state quantum phase transition through statistics of Loschmidt echo and quantum work
• Effects of excited state quantum phase transitions on system dynamics
• Phase transitions in the $sdg$ interacting boson model
• First-order quantum phase transitions: test ground for emergent chaoticity, regularity and persisting symmetries
• Excited state quantum phase transitions in the bending spectra of molecules
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• Calculation of Transition State Energies in the HCN-HNC Isomerization with an Algebraic Model
• Microscopic description of structural evolution in Pd, Xe, Ba, Nd, Sm, Gd and Dy isotopes
• The emergent dynamical symmetry at the triple point of nuclear deformations
• Excited State Quantum Phase Transitions Studied from a Non-Hermitian Perspective
• Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model
• Euclidean Dynamical Symmetry in Nuclear Shape Phase Transitions
• Excited-state quantum phase transitions in a two-fluid Lipkin model
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• Quantum catastrophes from an algebraic perspective
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