来自内部构型空间的广义空间群
Generalized Space Groups from Internal Configuration Spaces
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中文总结 AI 辅助
该研究提出了针对含非常规内部自由度晶体的广义空间群统一构造框架，以十二面体对象为例得到非平凡群对，其广义空间群含拓扑电荷为12的点节点，涵盖普通、磁性等空间群作为特例。
中文摘要 AI 辅助
我们针对具有非常规内部自由度的晶体，开发了广义空间群的统一构造方法。从允许的内部变换的完整群$G_P$以及参考对象的稳定子$P$出发，确定允许构型集的逐点对称性$J$和集合对称性$K$。随后利用古尔萨引理（Goursat's lemma）将内部商群$K/J$与空间商群耦合。该框架包含普通空间群、磁性空间群、自旋空间群和色空间群作为特例。作为示例，我们考虑$P=I\backsimeq A_5$的十二面体对象，得到非平凡对$T\triangleleft O$，其中$O/T\backsimeq\boldsymbol{Z}_2$。所得广义空间群具有拓扑电荷$|C|=12$的点节点。
英文摘要
We develop a unified construction of generalized space groups for crystals with unconventional internal degrees of freedom. Starting from the full group $G_P$ of allowed internal transformations and the stabilizer $P$ of a reference object, we determine the pointwise and setwise symmetries, $J$ and $K$, of the allowed configuration set. Goursat's lemma then couples the internal quotient $K/J$ to a spatial quotient. The framework includes ordinary, magnetic, spin, and color space groups as special cases. As an example, we consider a dodecahedral object with $P=I\simeq A_5$, for which we obtain the nontrivial pair $T\triangleleft O$ with $O/T\simeq\mathbb Z_2$. The resulting generalized space group hosts a point node with topological charge $|C|=12$.
