An analysis of localization transitions using non-parametric unsupervised learning

Carlo Vanoni, Vittorio Vitale

Published 2023-11-27Version 1

Localization transitions induced by disorder in quantum systems have been subject of intense discussion in the past decades. In particular, whether or not a localized phase is stable to the presence of interactions in the thermodynamic limit, is still an open question which is difficult to tackle both with numerical and analytical approaches. Here, we provide an alternative viewpoint by analyzing the classical encoding configurations of the disordered quantum system state and showing that its critical properties can be seen also as a geometric transition in data space. We showcase our approach on the Anderson model on regular random graphs, estimating the transition point in agreement with 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.