First-order quantum phase transitions: Test ground for emergent chaoticity, regularity and persisting symmetries

M. Macek*, A. Leviatan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT between spherical and deformed shapes, associated with its U(5) and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic dynamics reveals a rich but simply-divided phase space structure with a Hénon-Heiles type of chaotic dynamics ascribed to the spherical minimum and a robustly regular dynamics ascribed to the deformed minimum. The simple pattern of mixed but well-separated dynamics persists in the coexistence region and traces the crossing of the two minima in the Landau potential. A quantum analysis discloses a number of regular low-energy U(5)-like multiplets in the spherical region, and regular SU(3)-like rotational bands extending to high energies and angular momenta, in the deformed region. These two kinds of regular subsets of states retain their identity amidst a complicated environment of other states and both occur in the coexistence region. A symmetry analysis of their wave functions shows that they are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively. The pattern of mixed but well-separated dynamics and the PDS or QDS characterization of the remaining regularity, appear to be robust throughout the QPT. Effects of kinetic collective rotational terms, which may disrupt this simple pattern, are considered.

Original languageAmerican English
Pages (from-to)302-362
Number of pages61
JournalAnnals of Physics
StatePublished - 1 Dec 2014

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.


  • Interacting boson model (IBM)
  • Partial and quasi-dynamical symmetries
  • Quantum shape-phase transitions
  • Regularity and chaos


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