Inferring Hidden Symmetries of Exotic Magnets from Learning Explicit Order Parameters
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 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 work 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.