[en] The Anderson transition on random graphs is a paradigm for understanding high-dimensional quantum phase transitions driven by disorder and closely mirrors several features of many-body localization. In this Letter, we introduce a unitary Anderson model on small-world graphs, enabling large-scale, long-time simulations of wave-packet dynamics. This allows us to uncover logarithmically slow critical dynamics, two distinct localization times, and a crossover to ergodic diffusion. Finite-time scaling reveals distinct critical exponents, establishing a dynamical universality class for this exotic transition. Our model opens the way to an experimental realization of the Anderson transition on random graphs in quantum simulators. By combining disorder, high dimensionality, and dynamics, our approach provides a general framework for probing universal features of out-of equilibrium quantum phase transitions, including those relevant to many-body localization.
Disciplines :
Physics
Author, co-author :
Chen, Weitao; NUS - National University of Singapore > Department of Physics
García-Mata, Ignacio ; Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), CONICET–UNMdP, Funes 3350, B7602AYL Mar del Plata, Argentina
Martin, John ; Université de Liège - ULiège > Département de physique > Optique quantique
Jiangbin Gong; NUS - National University of Singapore > Department of Physics
Bertrand Georgeot; UPS - Université Toulouse 3 Paul Sabatier > CNRS, Laboratoire de Physique Théorique, Toulouse, France
Gabriel Lemarié; UniCA - Université Côte d'Azur > CNRS, INPHYNI, France
Language :
English
Title :
Critical Dynamics of the Anderson Transition on Small-World Graphs
Publication date :
14 April 2026
Journal title :
Physical Review Letters
ISSN :
0031-9007
eISSN :
1079-7114
Publisher :
American Physical Society (APS)
Volume :
136
Peer reviewed :
Peer Reviewed verified by ORBi
Funding text :
Consortium des Equipements de Calcul Intensif (CECI), funded by the Fonds de la Recherche Scientifique de Belgique (F. R. S.-FNRS) under Grant No. 2.5020.11
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