On the Symmetries of Anisotropic Spin Interaction Models
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910222007664640 |
|---|---|
| author | Yang, Arist Zhenyuan |
| author_facet | Yang, Arist Zhenyuan |
| contents | We show that anisotropic spin interactions do not merely break spin-space group (SSG) symmetries, but instead twist them through cohomology invariants, yielding symmetry classes beyond subgroups of $O(3)\times \operatorname{Isom}(\mathbb{R}^3) $. This requires redefining the spin-only group $S_0$ in terms of proper spin rotations. Based on this unitary $S_0$, we formulate a twisted SSG (tSSG) theory that captures the complete set of spin-space symmetries. We then study a spin-1 model with tSSG symmetry using linear flavor wave theory and find topological quadrupolar excitations defined on a spin Brillouin Klein-bottle rather than the conventional torus. Specifically, the bosonic BdG Hamiltonian satisfies a glide reflection sewing relation, the ribbon spectrum exhibits Möbius boundary states. These topological excitations are classified by $ \mathbb{Z}_2 $, enforced by the nonorientability of the Klein-bottle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14969 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Symmetries of Anisotropic Spin Interaction Models Yang, Arist Zhenyuan Strongly Correlated Electrons We show that anisotropic spin interactions do not merely break spin-space group (SSG) symmetries, but instead twist them through cohomology invariants, yielding symmetry classes beyond subgroups of $O(3)\times \operatorname{Isom}(\mathbb{R}^3) $. This requires redefining the spin-only group $S_0$ in terms of proper spin rotations. Based on this unitary $S_0$, we formulate a twisted SSG (tSSG) theory that captures the complete set of spin-space symmetries. We then study a spin-1 model with tSSG symmetry using linear flavor wave theory and find topological quadrupolar excitations defined on a spin Brillouin Klein-bottle rather than the conventional torus. Specifically, the bosonic BdG Hamiltonian satisfies a glide reflection sewing relation, the ribbon spectrum exhibits Möbius boundary states. These topological excitations are classified by $ \mathbb{Z}_2 $, enforced by the nonorientability of the Klein-bottle. |
| title | On the Symmetries of Anisotropic Spin Interaction Models |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.14969 |