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Fractal Geometry and Stochastics VIBreaking of Continuous Scale Invariance to Discrete Scale Invariance: A Universal Quantum Phase Transition

Fractal Geometry and Stochastics VI: Breaking of Continuous Scale Invariance to Discrete Scale... [We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete scale invariance. The rich features of this transition characterized by the abrupt formation of a geometric ladder of eigenstates, low energy universality without fixed points, scale anomalies and Berezinskii–Kosterlitz–Thouless scaling are described. The important role of this transition in various celebrated single and many body quantum systems is discussed along with recent experimental realizations. Particular focus is devoted to a recent realization in graphene.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Fractal Geometry and Stochastics VIBreaking of Continuous Scale Invariance to Discrete Scale Invariance: A Universal Quantum Phase Transition

Part of the Progress in Probability Book Series (volume 76)
Editors: Freiberg, Uta; Hambly, Ben; Hinz, Michael; Winter, Steffen
Ovdat, Omrie; Akkermans, Eric
Fractal Geometry and Stochastics VI — Mar 24, 2021
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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2021
ISBN
978-3-030-59648-4
Pages
209 –238
DOI
10.1007/978-3-030-59649-1_9
Publisher site
See Chapter on Publisher Site

Abstract

[We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete scale invariance. The rich features of this transition characterized by the abrupt formation of a geometric ladder of eigenstates, low energy universality without fixed points, scale anomalies and Berezinskii–Kosterlitz–Thouless scaling are described. The important role of this transition in various celebrated single and many body quantum systems is discussed along with recent experimental realizations. Particular focus is devoted to a recent realization in graphene.]

Published: Mar 24, 2021

Keywords: Discrete scale invariance; Continuous scale invariance; Universality; Limit cycles; Graphene; Berezinskii–Kosterlitz–Thouless; Primary: 28A80; Secondary: 28A75; 60G22

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