Machine learning wave functions to identify fractal phases

Author:

Tilen Cadez, Barbara Dietz, Dario Rosa, Alexei Andreanov, Keith Slevin, Tomi Ohtsuki

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

journal:

date:

2023-06-01 16:00:00

Abstract

We demonstrate that an image recognition algorithm based on a convolutional neural network provides a powerful procedure to differentiate between ergodic, non-ergodic extended (fractal) and localized phases in various systems: single-particle models, including random-matrix and random-graph models, and many-body quantum systems. The network can be successfully trained on a small data set of only 500 wave functions (images) per class for a single model. The trained network can then be used to classify phases in the other models and is thus very efficient. We discuss the strengths and limitations of the approach.

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