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  • Open Access

Symmetries of anisotropic spin interaction models

Arist Zhenyuan Yang*

  • Department of Physics and HK Institute of Quantum Science & Technology, The University of Hong Kong, Pokfulam Road, Hong Kong, China

  • *Contact author: zhenyuan@hku.hk
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Phys. Rev. Research 8, 033327 – Published 16 September, 2026

DOI: https://doi.org/10.1103/ywpn-pt91

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)×Isom(R3). This requires redefining the spin-only group S0 in terms of proper spin rotations. Based on this unitary S0, 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 Z2 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.

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Phys. Rev. Research 8, 033327– Published 16 September, 2026
  • Received 30 December 2025
  • Revised 27 March 2026
  • Accepted 1 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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