{
  "abstract": "Hidden-free-fermion (HFF) Hamiltonians exhibit free-fermion spectra despite lacking an explicit quadratic representation, yet their algebraic provenance and periodic-boundary behavior remain open questions. Here we establish that a broad class of HFF models arises from distinct Lax operator realizations of a twisted multistate Perk--Schultz \\(R\\) matrix. Its reflected degeneration generates a closed finite hierarchy of mutually commuting transfer matrices, whose functional relations determine the complete many-body spectrum. As a decisive example, we solve the inhomogeneous free-fermions-in-disguise (FFD) chain, which exhibits HFF, nested HFF, or interacting spectra, depending on its coupling. The homogeneous FFD chain with both one-wrap and periodic boundary conditions exhibits an emergent cubic finite-size gap while retaining the exact \\(z=3/2\\) bulk behavior. The construction extends to higher-state and face-type realizations, providing a common algebraic framework for coupling-dependent spectral organization and multiscale behavior in interacting quantum systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14134",
  "author_total": 3,
  "authors": [
    {
      "name": "Mingchen Zheng"
    },
    {
      "name": "Balázs Pozsgay"
    },
    {
      "name": "Shu Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7y2h1ckvw7ev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14134",
  "fulltext_url": null,
  "id": "a7y2h1ckvw7ev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14134",
  "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"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7213222349",
  "pdf_url": "https://arxiv.org/pdf/2609.14134",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7y2h1ckvw7ev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14134",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14134"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Exact solutions of hidden free fermion models",
  "title_text": "Exact solutions of hidden free fermion models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/a7y2h1ckvw7ev",
  "venue": "arXiv",
  "versions": []
}