{
  "abstract": "In this paper, we determine the complete ground-state spaces for a broad class of generalized stabilizer quantum models defined over CW-decompositions of non-compact manifolds of arbitrary dimensions and topological type. We introduce a $C^*$-algebraic framework in which the quantum spin algebra $\\A$ is realized as the twisted group $C^*$-algebra of an infinite discrete Pauli module $P$ endowed with a symplectic structure. We establish a correspondence between stabilizer models and isotropic subgroups of $P$: Every Lagrangian extension of such a subgroup determines a $C^*$-diagonal of $\\A$, whose Weyl groupoid encodes the dynamics through a continuous 1-cocycle. This realization yields an explicit family of extremal ground-states for every admissible Lagrangian model, together with their decomposition into sectors. When the sector space is $T_0$, this gives a complete characterization of the ground-state spaces. We also prove that every Lagrangian stabilizer model admits a unique frustration-free ground state with a spectral gap. Our framework applies in arbitrary dimension, including higher abelian quantum doubles, homological codes, and a broad class of stabilizer models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33221",
  "author_total": 4,
  "authors": [
    {
      "name": "Cathy Cheng"
    },
    {
      "name": "Nigel Higson"
    },
    {
      "name": "Danilo Polo Ojito"
    },
    {
      "name": "Emil Prodan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86bkfwe9nphkd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33221",
  "fulltext_url": null,
  "id": "86bkfwe9nphkd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33221",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223879837",
  "pdf_url": "https://arxiv.org/pdf/2610.33221",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/86bkfwe9nphkd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33221",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33221"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Ground-state spaces of generalized stabilizer codes",
  "title_text": "Ground-state spaces of generalized stabilizer codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/86bkfwe9nphkd",
  "venue": "arXiv",
  "versions": []
}