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arXiv:1904.09919

Intertwined Quantum Phase Transitions

N. Gavrielov, A. Leviatan, FRANCESCO IACHELLO

Published Apr 22, 2019• 0 citations
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Abstract

We introduce the notion of intertwined quantum phase transitions (IQPTs), for which shape-changes and configuration-changes in the ground state of a system are intertwined. We demonstrate the relevance of IQPTs to the Zr isotopes, where one of the most complex situations encountered in nuclear physics occurs, with coexisting Type I and Type II quantum phase transitions, and ground state shapes changing from spherical to prolate axially deformed and finally to gamma-unstable. Comparison with experimental data provides the first evidence for IQPTs in physical systems.

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We introduce the notion of intertwined quantum phase transitions (IQPTs), for which shape-changes and configuration-changes in the ground state of a system are intertwined. We demonstrate the relevance of IQPTs to the Zr isotopes, where one of the most complex situations encountered in nuclear physics occurs, with coexisting Type I and Type II quantum phase transitions, and ground state shapes changing from spherical to prolate axially deformed and finally to gamma-unstable. Comparison with experimental data provides the first evidence for IQPTs in physical systems.
Abstract Pronounced structural changes within individual configurations (Type I QPT), superimposed on an abrupt crossing of these configurations (Type II QPT), define the notion of intertwined quantum phase transitions (QPTs). We discuss and present evidence for such a scenario in finite Bose and Bose-Fermi systems. The analysis is based on algebraic models with explicit configuration mixing, where the two types of QPTs describe shape-phase transitions in-between different dynamical symmetries and shape-coexistence with crossing.
Quantum phase transitions (QPTs) in odd-mass Nb isotopes are investigated in the framework of the interacting boson-fermion model with configuration mixing. A quantum analysis reveals a Type I QPT (gradual shape-evolution within the intruder configuration) superimposed on a Type II QPT (abrupt crossing of normal and intruder states), thus demonstrating the occurrence of intertwined QPTs. A classical analysis highlights the implications for the single particle motion in the deformed field generated by the even-even Zr cores.
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.