Inferring hidden symmetries of exotic magnets from detecting explicit order parameters,Physical Review E

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Inferring hidden symmetries of exotic magnets from detecting explicit order parameters
Physical Review E ( IF 2.2 ) Pub Date : 2021-07-23 , DOI: 10.1103/physreve.104.015311
Nihal Rao _{1,

2} , Ke Liu _{1,

2} , Lode Pollet _{1,

2,

3}

Affiliation

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_{2 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.

中文翻译：

通过检测显式顺序参数推断奇异磁铁的隐藏对称性

通过高对称点的存在，可以将非常规磁铁映射到简单的铁磁体上。然后可以继承传统铁磁系统的知识，以深入了解更复杂的订单。在这里，我们展示了如何使用无监督和可解释的机器学习方法在非常规磁铁中搜索潜在的高对称点，而无需对系统有任何先验知识。该方法应用于蜂窝格子上的经典 Heisenberg-Kitaev 模型，我们的机器在其中学习显示其隐藏的变换