Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model

TL;DR

This study demonstrates that simple unsupervised machine learning methods, especially PCA, can effectively classify phases and identify localization regimes in the Falicov-Kimball model using Monte Carlo data.

Contribution

It shows that straightforward unsupervised techniques like PCA outperform complex methods in phase classification and localization crossover detection.

Findings

PCA successfully identifies phase boundaries.

Unsupervised methods distinguish localization regimes.

Simple techniques outperform complex neural network approaches.

Abstract

We apply various unsupervised machine learning methods for phase classification to investigate the finite-temperature phase diagram of the spinless Falicov-Kimball model in two dimensions. Using only particle occupation snapshots from Monte Carlo simulations as input, each technique, including a straightforward classification based on principal component analysis (PCA), successfully identifies the phase boundary between ordered and disordered phases, independent of the type of phase transition. Remarkably, these techniques also distinguish between the weakly localized and Anderson-localized regimes within the disordered phase, accurately identifying their crossover, which is a challenging task for standard methods. Among the machine learning approaches used, PCA based analysis outperforms more complex methods, such as neural network predictors and autoencoders. These results underscore the effectiveness of simple unsupervised techniques in examining phase transitions and electron localization in complex correlated systems.