An analysis of localization transitions using non-parametric unsupervised learning

Abstract

We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded configurations of the disordered quantum system. We showcase our approach to the Anderson model on regular random graphs, known for displaying features of interacting systems, despite being a single-particle problem. We estimate the transition point and critical exponents in agreement with the best-known results in the literature. We provide a simple and coherent explanation of our findings, discussing the applicability of the method in real-world scenarios with a modest number of measurements.

5+5 pages, 7 figures. Major improvements in v2. Comments are welcome!

References in corpus (5)

• Thermalization and its mechanism for generic isolated quantum systems
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• How a small quantum bath can thermalize long localized chains
• Critical behavior at the localization transition on random regular graphs

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