Machine learning wave functions to identify fractal phases

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

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arXiv · 2306.01402

Machine learning wave functions to identify fractal phases

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

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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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BibTeX RIS

Tilen Cadez, Barbara Dietz, Dario Rosa, Alexei Andreanov, Keith Slevin, Tomi Ohtsuki. 2023-06-02. Machine learning wave functions to identify fractal phases. https://arxiv.org/abs/2306.01402

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