The breaking of continuous scale invariance to discrete scale invariance: a universal quantum phase transition
Mesoscale and Nanoscale Physics
2021-04-15 v1 Mathematical Physics
math.MP
Quantum Physics
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 is 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.
Keywords
Cite
@article{arxiv.1909.05505,
title = {The breaking of continuous scale invariance to discrete scale invariance: a universal quantum phase transition},
author = {Omrie Ovdat and Eric Akkermans},
journal= {arXiv preprint arXiv:1909.05505},
year = {2021}
}
Comments
Contribution to the conference 'Fractal Geometry and Stochastics 6' proceedings. 20 pages, 8 figures, 2 tables