{
  "abstract": "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 $\\mathbb{Z}_2$ topological quadrupolar excitations defined on a spin Brillouin Klein bottle. Specifically, the quadrupolar excitations possess a momentum-space glide-reflection symmetry and the edge states exhibit a nonlocal momentum twist. These results establish the symmetry language required for interacting spin systems, whether realized in magnetic materials or on programmable quantum simulators, and open a route to unconventional magnetism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. Research 8, 033327 (2026)",
  "arxiv": "2605.14969",
  "author_total": 1,
  "authors": [
    {
      "name": "Arist Zhenyuan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0j0qam59ymk0c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.14969",
  "fulltext_url": null,
  "id": "0j0qam59ymk0c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.14969",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.14969",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0j0qam59ymk0c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2605.14969",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.14969"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "On the Symmetries of Anisotropic Spin Interaction Models",
  "title_text": "On the Symmetries of Anisotropic Spin Interaction Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/0j0qam59ymk0c",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/ywpn-pt91",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}