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Physica Scripta

Quantum phase transitions in the collective degrees of freedom: nuclei and other many-body systems

Pavel Cejnar, Pavel Stránský

Published Jul 18, 2016• 18 citations
Publisher

Abstract

Abstract Quantum phase transitions (QPTs) represent a quickly developing subject of theoretical and experimental research. Nuclear physics contributed to the formation of the QPT concept in the 1970s and remains an area where new viewpoints and original approaches to criticality in many-body systems can be created. In this review, we present a comprehensible introduction to the subject, with an emphasis on the role of nuclear physics, and point out some specific features of QPTs in the systems that exhibit an effective separation of some collective degrees of freedom. The focus on collectivity, which stems from the nuclear context, is an essential ingredient of our treatise. It leads to some consequences that find application in nuclei as well as in a wide spectrum of non-nuclear systems.

DOI
10.1088/0031-8949/91/8/083006

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Abstract Quantum phase transitions (QPTs) represent a quickly developing subject of theoretical and experimental research. Nuclear physics contributed to the formation of the QPT concept in the 1970s and remains an area where new viewpoints and original approaches to criticality in many-body systems can be created. In this review, we present a comprehensible introduction to the subject, with an emphasis on the role of nuclear physics, and point out some specific features of QPTs in the systems that exhibit an effective separation of some collective degrees of freedom. The focus on collectivity, which stems from the nuclear context, is an essential ingredient of our treatise. It leads to some consequences that find application in nuclei as well as in a wide spectrum of non-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.
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In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d -wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.