{
  "abstract": "We investigate a hierarchy of invariant Hilbert-space structures connecting Hilbert-space fragmentation, partial solvability, and quantum many-body scars. For spin chains with fragmented spin-$1/2$ subspaces and their local deformations, we show, using the spin-$1$ $XXC$ chain as a representative example, how successive local deformations reduce extensive irreducible-string fragmentation through an implicitly embedded spin-$1/2$ invariant space and ultimately to a single scar tower, connecting the $XXC$, perturbed $XXC$, and spin-$1$ $XY$ scar models. Through the intermediate embedded space, local dynamics couples states from distinct frozen irreducible-string sectors and selects a new decomposition into representations, from which smaller invariant spaces can be retained. We also establish a rigidity constraint on isolating nonsymmetric towers and a constructive correspondence that transfers a reduction between locally realizable representations of the embedded dynamics. The latter demonstrates that the reduction hierarchy can be transferred through a unitary transformation within the embedded subspace, yielding an exact scar tower built on a Néel reference state without requiring unitary equivalence of the full Hamiltonians.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30597",
  "author_total": 1,
  "authors": [
    {
      "name": "Chihiro Matsui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejmk320jw00yg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30597",
  "fulltext_url": null,
  "id": "ejmk320jw00yg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30597",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7223405483",
  "pdf_url": "https://arxiv.org/pdf/2610.30597",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejmk320jw00yg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30597",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30597"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Hierarchical Reduction of Invariant Subspaces: From Fragmentation to Many-Body Scars",
  "title_text": "Hierarchical Reduction of Invariant Subspaces: From Fragmentation to Many-Body Scars",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/ejmk320jw00yg",
  "venue": "arXiv",
  "versions": []
}