Unsupervised machine learning of quenched gauge symmetries: A proof-of-concept demonstration

Abstract

One of the most prominent tasks of machine learning (ML) methods within the field of condensed matter physics has been to classify phases of matter. Given their many successes in performing this task, one may ask whether these methods---particularly unsupervised ones---can go beyond learning the thermodynamic behavior of a system. This question is especially intriguing when considering systems that have a ``hidden order''. In this work we study two random spin systems with a hidden ferromagnetic order that can be exposed by applying a Mattis gauge transformation. We demonstrate that the principal component analysis, perhaps the simplest unsupervised ML method, can detect the hidden order, quantify the corresponding gauge variables, and map the original random models onto simpler gauge-transformed ferromagnetic ones, all without any prior knowledge of the underlying gauge transformation. Our work illustrates that ML algorithms can in principle identify not manifestly obvious symmetries of a system.