从显式序参量推断奇异磁体的隐对称性
Inferring Hidden Symmetries of Exotic Magnets from Detecting Explicit Order Parameters
摘要：
一个非常规的磁铁可以通过一个高对称点的存在映射到一个简单的铁磁体上。传统的铁磁系统的知识，然后可以结转，以提供洞察更复杂的订单。在这里，我们演示了如何使用无监督和可解释的机器学习方法来搜索非常规磁体中的潜在高对称点，而无需任何系统的先验知识。该方法被应用到蜂窝晶格上的经典Heisenberg-Kitaev模型，其中我们的机器学习体现其隐藏的$O(3)$对称性的变换，而不使用这些高对称点的数据。此外，我们澄清，在对比条纹和锯齿状订单，一组$D_2$和$D_{2h}$排序矩阵提供了一个更完整的描述的磁化海森堡-Kitaev模型。此外，我们的机器还学习了相边界处的局部约束，这表明了亚维对称性。本文强调了显式序参量对多体自旋系统的重要性以及机器学习技术在物理应用中的可解释性。
英文摘要：
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.
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