Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks

TL;DR

This paper demonstrates that Generative Adversarial Networks can detect Berezinskii-Kosterlitz-Thouless phase transitions in quantum systems by analyzing entanglement spectra, offering a machine learning approach with minimal prior knowledge.

Contribution

It introduces a GAN-based method to identify phase transitions in quantum many-body systems using entanglement spectra, advancing anomaly detection in phase diagram analysis.

Findings

GAN successfully detects gapless-to-gapped transitions

Method requires minimal prior knowledge

Potential for broader application in phase diagram studies

Abstract

The detection of phase transitions in quantum many-body systems with lowest possible prior knowledge of their details is among the most rousing goals of the flourishing application of machine-learning techniques to physical questions. Here, we train a Generative Adversarial Network (GAN) with the Entanglement Spectrum of a system bipartition, as extracted by means of Matrix Product States ans\"atze. We are able to identify gapless-to-gapped phase transitions in different one-dimensional models by looking at the machine inability to reconstruct outsider data with respect to the training set. We foresee that GAN-based methods will become instrumental in anomaly detection schemes applied to the determination of phase-diagrams.