{
  "abstract": "We construct translation-invariant pure quasifree fermionic states on the one-dimensional lattice whose half-chain von Neumann algebras are hyperfinite factors of type $\\mathrm{II}_\\infty$ or $\\mathrm{III}_λ$ for any $0<λ\\leq 1$. Via the Jordan-Wigner-Araki transformation, these yield translation-invariant pure spin-chain states with the same half-chain factors, demonstrating that such factors need not be of type I or III. Each state is the unique ground state of a gapless, translation-invariant parent Hamiltonian with superpolynomially decaying interactions. For any fixed factor type, the interval entanglement entropy can exhibit widely varying growth rates, from arbitrarily slow divergence to nearly power-law growth, showing that entropy scaling does not determine the factor type. In contrast, we prove that gauge-invariant quadratic Hamiltonians with finitely many flavours and exponentially decaying hopping exhibit a dichotomy: their ground states either satisfy an area law with a type I half-chain factor, or have logarithmic entropy growth with a type $\\mathrm{III}_1$ factor. The counterexample was discovered with AI assistance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24154",
  "author_total": 2,
  "authors": [
    {
      "name": "Ruizhi Liu"
    },
    {
      "name": "Jinmin Yi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3p9c93ce5sq3g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24154",
  "fulltext_url": null,
  "id": "3p9c93ce5sq3g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24154",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7223048298",
  "pdf_url": "https://arxiv.org/pdf/2610.24154",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3p9c93ce5sq3g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24154",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24154"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Translation-Invariant Pure States with Exotic Half-Chain Factors",
  "title_text": "Translation-Invariant Pure States with Exotic Half-Chain Factors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/3p9c93ce5sq3g",
  "venue": "arXiv",
  "versions": []
}