Self-Supervised Ensemble Learning: A Universal Method for Phase Transition Classification of Many-Body Systems

TL;DR

This paper introduces a self-supervised ensemble learning method capable of classifying various phase transitions in many-body systems using spin configurations, applicable to classical and quantum models without prior theoretical knowledge.

Contribution

The paper presents a novel self-supervised ensemble learning approach that accurately classifies different phase transitions, including quantum ones, by analyzing fluctuation properties of machine learning outputs.

Findings

Successfully classifies first-order, second-order, and BKT transitions in classical models.

Extends to quantum phase transitions in 1D Ising and XXZ models.

Provides richer information than previous machine learning methods.

Abstract

We develop a self-supervised ensemble learning (SSEL) method to accurately classify distinct types of phase transitions by analyzing the fluctuation properties of machine learning outputs. Employing the 2D Potts model and the 2D Clock model as benchmarks, we demonstrate the capability of SSEL in discerning first-order, second-order, and Berezinskii-Kosterlitz-Thouless transitions, using in-situ spin configurations as the input features. Furthermore, we show that the SSEL approach can also be applied to investigate quantum phase transitions in 1D Ising and 1D XXZ models upon incorporating quantum sampling. We argue that the SSEL model simulates a special state function with higher-order correlations between physical quantities, and hence provides richer information than previous machine learning methods. Consequently, our SSEL method can be generally applied to the identification/classification of phase transitions even without explicit knowledge of the underlying theoretical models.