2026/08/05 by Zeying Zhang, Zhenye Li, Zhi-Ming Yu +2
Physics and Astronomy · #cond-mat.mtrl-sci
6 pages, 2 figures
arxiv created 2026/08/05 · arxiv updated 2026/08/06
We develop a unified construction of generalized space groups for crystals with unconventional internal degrees of freedom. Starting from the full group GP 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≃ A5, for which we obtain the nontrivial pair T\triangleleft O with O/T≃\mathbb Z2. The resulting generalized space group hosts a point node with topological charge |C|=12.