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.
Highlights
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
We show that our method provides an efficient and versatile approach to detect high-symmetry points hidden in unconventional magnets
We demonstrated that tensorial-kernel support vector machine (TK-support vector machines (SVMs)) provides a data-driven approach to the problem of identifying hidden symmetries in phases with unconventional magnetic orders
Summary
Applications of machine learning in different fields of physics have become ubiquitous and witnessed a dramatic rise in the past few years [1,2], ranging from statistical physics [3,4], condensed matter physics [5,6,7], chemistry and material science [8,9,10], to high energy physics [11,12,13] and quantum computation [14,15,16]. Hidden symmetries are of broad relevance and rich in physics, identifying them is a nontrivial task and is very much problem dependent, often requiring remarkable insights and experience from researchers It would be interesting and useful if machine-learning techniques can facilitate their identification. We use a machine-learning method, the tensorial-kernel support vector machine (TK-SVM) [41,42,43], to find potential hidden symmetries in a spin model.
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