{
  "abstract": "We show that SYK-like melonic solvability and maximal chaos survive in a sparse deterministic model, without disorder averaging. Our deterministic hypergraph SYK model (hSYK) consists of $N$ Majorana fermions on a $q$-uniform, $d$-regular interaction hypergraph with only $O(dN)$ interaction terms and uniform positive couplings. Under explicit geometric and spectral expansion conditions, its two-point function satisfies the standard melonic Schwinger-Dyson equation up to $O(d^{-1})$ corrections, while the leading bilocal effective action coincides with that of ordinary SYK at the dominant large-$d$ saddle. Its connected four-point function factorizes into a temporal SYK ladder kernel and a line-graph random walk. A finite line-graph spectral gap controls the visibility of the maximally chaotic uniform mode in generic localized OTOCs and, by gapping non-uniform spatial modes in the bilocal spectrum, excludes additional light fluctuation modes beyond the Schwarzian. Exact diagonalization further shows melonic two-point scaling, single-instance Wigner-Dyson statistics, and the predicted graph-controlled spatial decay of OTOCs. The model therefore offers a disorder-free realization of the essential melonic and chaotic features of SYK, in a form more amenable to quantum simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19255",
  "author_total": 1,
  "authors": [
    {
      "name": "Shiroman Prakash"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/de67zg5rreavc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19255",
  "fulltext_url": null,
  "id": "de67zg5rreavc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19255",
  "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.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7213609661",
  "pdf_url": "https://arxiv.org/pdf/2609.19255",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/de67zg5rreavc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19255",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19255"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Deterministic Hypergraph SYK: Melonic Dominance and Maximal Chaos Without Disorder Averaging",
  "title_text": "Deterministic Hypergraph SYK: Melonic Dominance and Maximal Chaos Without Disorder Averaging",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/de67zg5rreavc",
  "venue": "arXiv",
  "versions": []
}