A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models

TL;DR

This paper explores how neural networks can accurately identify the Berezinskii-Kosterlitz-Thouless transition in various classical and quantum models, addressing the challenge of pinpointing the critical temperature due to smooth thermodynamic quantities.

Contribution

It introduces a neural network-based method for detecting the BKT transition across different classical and quantum systems, analyzing training strategies for improved accuracy.

Findings

Neural networks can effectively identify the BKT transition.

Training method impacts the accuracy of transition detection.

Applicable to classical and quantum models.

Abstract

The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we demonstrate how neural networks can be used to perform this task. In particular, we study how the accuracy of the transition identification depends on the way the neural networks are trained. We apply our approach to three different systems: (i) the classical XY model, (ii) the phase-fermion model, where classical and quantum degrees of freedom are coupled and (iii) the quantum XY model.