{
  "abstract": "Area laws express the expectation that entanglement in gapped quantum ground states scales with a boundary rather than a volume. In one dimension this holds for every Rényi entropy, and the Rényi area-law conjecture asserts the same in higher dimensions for each fixed $0<α<1$. Here we disprove this conjecture in every spatial dimension two and higher. We construct finite-range Hamiltonians with fixed local dimension, bounded interaction strength, unique ground states and a uniform spectral gap, whose ground states exhibit volume-law Rényi entanglement while obeying a von Neumann area law and remaining connected to product states through uniformly gapped local paths. The mechanism is error-space complexity: locally identifiable components of arbitrarily small weight can encode states with high entanglement complexity. We also establish the worst-case rank-error trade-off for approximate ground-state projectors, a key tool in one-dimensional area-law proofs. At fixed gap, the optimal Schmidt rank at projection error $ε$ across a planar cut of cross-section $A$ scales as $\\exp[\\tildeΘ((A\\logε^{-1})^{2/3})]$ when $\\logε^{-1}\\gtrsim A$. Thus $α=1$ is the sharp threshold for a universal Rényi area law within this adiabatically connected class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15199",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomotaka Kuwahara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1samj8bcmab61.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15199",
  "fulltext_url": null,
  "id": "1samj8bcmab61",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15199",
  "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.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7221766223",
  "pdf_url": "https://arxiv.org/pdf/2610.15199",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1samj8bcmab61.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15199",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15199"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The Rényi area law conjecture is false below $α=1$ in high dimensions",
  "title_text": "The Rényi area law conjecture is false below α=1 in high dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1samj8bcmab61",
  "venue": "arXiv",
  "versions": []
}