Machine-Learning Study using Improved Correlation Configuration and Application to Quantum Monte Carlo Simulation

TL;DR

This paper introduces an improved correlation estimator based on the Fortuin-Kasteleyn representation for machine learning phase classification in spin models, successfully applying it to quantum Monte Carlo simulations of the XY model.

Contribution

It presents a novel estimator for correlation configurations that enhances machine learning classification of phases, including quantum phases, using classical training data.

Findings

Effective classification of BKT and paramagnetic phases in quantum XY model.

The method works with classical training data to classify quantum phases.

Improved estimators enhance machine learning accuracy in spin models.

Abstract

We use the Fortuin-Kasteleyn representation based improved estimator of the correlation configuration as an alternative to the ordinary correlation configuration in the machine-learning study of the phase classification of spin models. The phases of classical spin models are classified using the improved estimators, and the method is also applied to the quantum Monte Carlo simulation using the loop algorithm. We analyze the Berezinskii-Kosterlitz-Thouless (BKT) transition of the spin 1/2 quantum XY model on the square lattice. We classify the BKT phase and the paramagnetic phase of the quantum XY model using the machine-learning approach. We show that the classification of the quantum XY model can be performed by using the training data of the classical XY model.