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arXiv · 2608.03808

Generalized Space Groups from Internal Configuration Spaces

Zeying Zhang·Zhenye Li·Zhi-Ming Yu·Gui-Bin Liu·Yugui Yao
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Abstract

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 $|C|=12$.

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Zeying Zhang, Zhenye Li, Zhi-Ming Yu, Gui-Bin Liu, Yugui Yao. 2026-08-04. Generalized Space Groups from Internal Configuration Spaces. https://arxiv.org/abs/2608.03808

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