Inferring hidden symmetries of exotic magnets from detecting 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 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 D2 and D2 h 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.
- Publication:
-
Physical Review E
- Pub Date:
- July 2021
- DOI:
- 10.1103/PhysRevE.104.015311
- arXiv:
- arXiv:2007.07000
- Bibcode:
- 2021PhRvE.104a5311R
- Keywords:
-
- Physics - Computational Physics;
- Condensed Matter - Materials Science;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 12 pages, 14 figures, 1 table