Berezinskii-Kosterlitz-Thouless transition from Neural Network Flows

TL;DR

This paper uses neural network flows, specifically variational autoencoders, to identify the Berezinskii-Kosterlitz-Thouless phase transition in a 2D clock model by analyzing fixed-point ensembles with a novel JSD thermometer.

Contribution

It introduces a neural network flow approach with a JSD-based thermometer to detect BKT transitions in the 2D clock model, providing a new unsupervised method for phase transition analysis.

Findings

NN flow converges to fixed-point ensembles at different temperatures.

JSD profiles of fixed points reveal critical temperatures of BKT transitions.

Method offers a new way to identify phase transitions without explicit order parameters.

Abstract

We adopt the neural network flow (NN flow) method to study the Berezinskii-Kosterlitz-Thouless (BKT) phase transitions of the 2-dimensional q-state clock model with $q\ge 4$. The NN flow consists of a sequence of the same units to proceed the flow. This unit is a variational autoencoder (VAE) trained by the data of Monte-Carlo configurations in the way of unsupervised learning. To gauge the difference among the ensembles of Monte-Carlo configurations at different temperatures and the uniqueness of the ensemble of NN-flowed states, we adopt the Jesen-Shannon divergence (JSD) as the information-distance measure "thermometer". This JSD thermometer compares the probability distribution functions of the mean magnetization of two ensembles of states. Our results show that the NN flow will flow an arbitrary spin state to some state in a fixed-point ensemble of states. The corresponding JSD of the fixed-point ensemble takes a unique profile with peculiar features, which can help to identify the critical temperatures of BKT phase transitions of the underlying Monte-Carlo configurations.