Inferring Hidden Symmetries of Exotic Magnets from Detecting Explicit Order Parameters

TL;DR

This paper introduces an unsupervised machine-learning method to identify high-symmetry points and hidden symmetries in unconventional magnets, specifically applied to the Heisenberg-Kitaev model, revealing new insights into magnetic order parameters.

Contribution

The study presents a novel interpretable machine-learning approach to detect high-symmetry points and hidden symmetries in complex magnetic systems without prior knowledge.

Findings

Machine learns the $O(3)$ symmetry transformations in the Heisenberg-Kitaev model.

A set of $D_2$ and $D_{2h}$ matrices better describes magnetization than traditional orders.

Local constraints at phase boundaries reveal subdimensional symmetry.

Abstract

An unconventional magnet may be mapped onto a simple ferromagnet by the existence of a high-symmetry point. Knowledge of conventional ferromagnetic systems may then be carried over to provide insight into more complex orders. Here we demonstrate how an unsupervised and interpretable machine-learning approach can be used to search for potential high-symmetry points in unconventional magnets without any prior knowledge of the system. The method is applied to the classical Heisenberg-Kitaev model on a honeycomb lattice, where our machine learns the transformations that manifest its hidden $O(3)$ symmetry, without using data of these high-symmetry points. Moreover, we clarify that, in contrast to the stripy and zigzag orders, a set of $D_2$ and $D_{2h}$ ordering matrices provides a more complete description of the magnetization in the Heisenberg-Kitaev model. In addition, our machine also learns the local constraints at the phase boundaries, which manifest a subdimensional symmetry. This paper highlights the importance of explicit order parameters to many-body spin systems and the property of interpretability for the physical application of machine-learning techniques.