{
  "abstract": "We introduce a graph invariant obtained from Pauli decompositions of Hamiltonians derived from local graph neighborhoods. Given a rooted h-hop neighborhood, we construct a local adjacency operator, embed it into a common Hilbert space dimension, and define its Pauli-support set as the collection of Pauli strings appearing with nonzero coefficients. For periodic graphs, we prove invariance under lattice-compatible graph equivalence and establish converse results under root-separation hypothesis. The framework naturally extends to Lie closures, commutants, and Cartan-type structures generated by the associated Pauli supports. We further discuss extensions to aperiodic graphs with finite local complexity and make connections to cut-and-project models of quasicrystals and notably, Penrose tilings. From a quantum information perspective, the resulting invariants provide a operator-theoretic description of graph-based Hamiltonians and offer a new mechanism for comparing graph-based quantum systems through Pauli-support data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14209",
  "author_total": 4,
  "authors": [
    {
      "name": "Sarah Chehade"
    },
    {
      "name": "Andrew Vlasic"
    },
    {
      "name": "Rebekah Herrman"
    },
    {
      "name": "Rick Mukherjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8k57q9vdfbspj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14209",
  "fulltext_url": null,
  "id": "8k57q9vdfbspj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14209",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2505|Quasicrystal Structures and Properties"
    ]
  ],
  "openalex": "W7213247235",
  "pdf_url": "https://arxiv.org/pdf/2609.14209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8k57q9vdfbspj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14209"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Pauli Supported Invariants for Periodic Graphs-Derived Hamiltonians",
  "title_text": "Pauli Supported Invariants for Periodic Graphs-Derived Hamiltonians",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/8k57q9vdfbspj",
  "venue": "arXiv",
  "versions": []
}