{
  "abstract": "Characterizing local Hamiltonians that host interesting many-body states as eigenstates has been an important problem in quantum many-body physics. For matrix product states (MPS), there is a well-known construction of parent Hamiltonians that have the MPS as the frustration-free ground state. However, recent results on quantum many-body scars have shown that such a construction does not exhaust all possible Hamiltonians that have the MPS as an eigenstate. In this work, we develop an exhaustive construction of generalized parent Hamiltonians that have a given translation-invariant MPS as an eigenstate. These go beyond the conventional projector-based construction of frustration-free parent Hamiltonians, where each local Hermitian term has the MPS as an eigenstate, by allowing non-Hermitian telescoping terms that cancel out with periodic boundary conditions (PBC). We derive a local tensor equation that establishes a correspondence between inequivalent classes of generalized parent Hamiltonians, i.e., those that cannot be related using linear combinations with frustration-free Hamiltonians, and the MPS transfer matrix spectrum. We illustrate the connection to intrinsic physical properties, including non-Abelian symmetries and zero correlation length, and further extend this construction to block-injective MPS. Our framework hence provides a systematic bridge between generalized parent Hamiltonians and the local structure of quantum states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00203",
  "author_total": 3,
  "authors": [
    {
      "name": "He-Ran Wang"
    },
    {
      "name": "Lorenzo Gotta"
    },
    {
      "name": "Sanjay Moudgalya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5gta350cef5jb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00203",
  "fulltext_url": null,
  "id": "5gta350cef5jb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00203",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00203",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5gta350cef5jb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00203",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00203"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Exhaustive Construction of Generalized Parent Hamiltonians for Matrix Product States",
  "title_text": "Exhaustive Construction of Generalized Parent Hamiltonians for Matrix Product States",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/5gta350cef5jb",
  "venue": "arXiv",
  "versions": []
}