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arXiv:cond-mat/9809200

Phase Transitions in Condensed Matter and Relativistic QFT

R. J. Rivers

Published Sep 14, 1998• 0 citations
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Abstract

Kibble and Zurek have provided a unifying picture for the onset of phase transitions in relativistic QFT and condensed matter systems respectively, strongly supported by agreement with condensed matter experiments in He3. The failure of a recent experiment on He4 to agree with the predictions has prompted a reappraisal of this picture. We provide an alternative picture that explains the experimental evidence.

DOI
10.48550/arxiv.cond-mat/9809200

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Kibble and Zurek have provided a unifying picture for the onset of phase transitions in relativistic QFT and condensed matter systems respectively, strongly supported by agreement with condensed matter experiments in He3. The failure of a recent experiment on He4 to agree with the predictions has prompted a reappraisal of this picture. We provide an alternative picture that explains the experimental evidence.
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Half a century ago, T. Kibble proposed a scenario for topological defect formation from symmetry breaking during the expansion of the early Universe. W. Zurek later crystallized the concept to superfluid helium, predicting a power-law relation between the number of quantum vortices and the rate at which the system passes through the lambda transition. Here, we report the observation of Kibble-Zurek scaling in a homogeneous, strongly interacting Fermi gas undergoing a superfluid phase transition. We investigate the superfluid transition using two distinct control parameters: temperature and interaction strength. The microscopic physics of condensate formation is markedly different for the two quench parameters, signaled by their two orders of magnitude difference in the condensate formation timescale. However, regardless of the thermodynamic direction in which the system passes through a phase transition, the Kibble-Zurek exponent is identically observed to be about 0.68 and shows good agreement with theoretical predictions that describe superfluid phase transitions. This work demonstrates the gedanken experiment Zurek proposed for liquid helium that shares the same universality class with strongly interacting Fermi gases.
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.