{
  "abstract": "Starting from the cyclic duality tensors introduced by Vernier, Miao, and Yamazaki (VMY), whose endpoint-traced matrix-product operators obey $\\mathbb Z_N$ Tambara--Yamagami fusion and realize topological defect lines of the compactified-boson conformal field theory, we retain the virtual endpoint as an $N$-state dynamical degree of freedom and construct an exactly movable seam in the spin-$\\tfrac12$ XXZ chain at $q=\\mathrm e^{\\mathrm iπM/N}$ with $\\gcd(M,N)=1$. The local movement identity holds for any unitary $q$-Weyl pair; in the finite cyclic realization, all output phases are locally gauge equivalent and share the same four seam eigenvalues. On a ring, the output gauge becomes a directed twist on a single bond, while endpoint conjugacy reduces the $2N$ labels to two relative $\\mathbb Z_2$ flux classes. An explicit antiunitary symmetry protects the class $η\\equiv M-1\\pmod 2$: for even $N$ it pairs distinct charge sectors isospectrally, whereas for odd $N$ it fixes one sector and squares to $-I$ there. Hence every many-body energy eigenspace in the protected class has even multiplicity. The source value $η_{\\rm VMY}=1-M$ satisfies this condition for every coprime root, whereas the ungauged value $η=0$ does so only for odd $M$. Exact finite-size controls show that the opposite class can contain simple levels, so a global flux invisible to local gauge equivalence distinguishes the two classes spectrally.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27940",
  "author_total": 3,
  "authors": [
    {
      "name": "Boliang Yu"
    },
    {
      "name": "Ruixin Zhou"
    },
    {
      "name": "Meisen Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/armfnk6deyxkk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27940",
  "fulltext_url": null,
  "id": "armfnk6deyxkk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27940",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7214225721",
  "pdf_url": "https://arxiv.org/pdf/2609.27940",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/armfnk6deyxkk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27940",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27940"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Movable seams in root-of-unity XXZ chains: Relative flux classes and antiunitary spectral pairing",
  "title_text": "Movable seams in root-of-unity XXZ chains: Relative flux classes and antiunitary spectral pairing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/armfnk6deyxkk",
  "venue": "arXiv",
  "versions": []
}