Interpretable and unsupervised phase classification based on averaged input features

Fully automated classification of phases from observations is of paramount importance to physics. Significant effort has recently been made to render this classification unsupervised and interpretable. Here, we present a physically motivated, computationally cheap, unsupervised, and interpretable method to infer phase boundaries from data [1]. The method relies on the difference between mean input features as an indicator for phase transitions and does not utilize predictive models. Crucially, this mean-based approach allows for direct physical insights into the revealed phase diagram without prior labelling or knowledge of its phases. As an example, we consider the physically rich ground-state phase diagram of the spinless Falicov-Kimball model. The large number of phases makes the analysis of this phase diagram by standard methods a hard task. In particular, supervised methods are bound to fails because phase labels are not known beforehand. We demonstrate that the mean-based method works well in this setting.

[1] J. Arnold, F. Schäfer, M. Zonda, and A. U. J. Lode, arXiv:2010.04730 (2020).