Mapping out phase diagrams with generative classifiers

Abstract

One of the central tasks in many-body physics is the determination of phase diagrams. However, mapping out a phase diagram generally requires a great deal of human intuition and understanding. To automate this process, one can frame it as a classification task. Typically, classification problems are tackled using discriminative classifiers that explicitly model the probability of the labels for a given sample. Here we show that phase-classification problems are naturally suitable to be solved using generative classifiers based on probabilistic models of the measurement statistics underlying the physical system. Such a generative approach benefits from modeling concepts native to the realm of statistical and quantum physics, as well as recent advances in machine learning. This leads to a powerful framework for the autonomous determination of phase diagrams with little to no human supervision that we showcase in applications to classical equilibrium systems and quantum ground states.

7+9 pages, 3+5 figures; improved presentation and included numerical evidence supporting claims of computational efficiency

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• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders