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  "slug": "kagome-aklt-spectral-gap",
  "title": "A finite certificate for a kagome quantum gap",
  "shortTitle": "The spin-2 kagome AKLT gap",
  "url": "https://evidencepress.org/releases/kagome-aklt-spectral-gap/",
  "oneLine": "A grouped local test gives a size-independent lower energy gap for a specified kagome quantum-spin model.",
  "abstract": "A deterministic computer-assisted proof candidate gives gap(H) ≥ 11(2−√3)(59−3√313)/3360 > 0.0051 for the spin-2 AKLT model, with total-spin-four edge projectors, on rectangular kagome tori m,n≥3 and finite unions of complete down-star edge sets. Exact rational tensors and 54 validated positivity tests feed a written local-to-global argument. Arithmetic and semantic assumptions remain explicit; no arbitrary-boundary or perturbative-stability theorem is claimed.",
  "datePublished": "2026-09-30",
  "dateModified": "2026-09-30",
  "version": "0.3.1-candidate",
  "doi": "10.5281/zenodo.23070704",
  "doiUrl": "https://doi.org/10.5281/zenodo.23070704",
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  "repoUrl": "https://github.com/ipitchford/kagome-aklt-spectral-gap",
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      "name": "A Finite Certificate For A Kagome Quantum Gap",
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  "authors": [
    "Anonymous"
  ],
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  "problem": {
    "name": "Uniform spectral gap of the spin-2 kagome AKLT model",
    "url": "https://arxiv.org/abs/2010.03137"
  },
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  "metadataProvenance": "Supplied candidate and model-assisted review revised 30 September 2026; external reviewer independence is not authenticated.",
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  "keywords": [
    "AKLT model",
    "kagome lattice",
    "spectral gap",
    "quantum spin systems",
    "validated numerics",
    "computer-assisted proof"
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  "keyResults": [
    "Uniform lower gap greater than 0.0051 for the stated finite volumes.",
    "Sector-dependent two-plus-one grouping succeeds where the pair-only threshold does not.",
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    "Investigate sharper local inequalities without confusing a validation margin with the physical spectral gap.",
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  "relatedWorks": [
    {
      "citation": "Affleck, Kennedy, Lieb and Tasaki (1988), Valence bond ground states in isotropic quantum antiferromagnets: model background.",
      "url": "https://doi.org/10.1007/BF01218021",
      "doi": "10.1007/BF01218021"
    },
    {
      "citation": "Guo, Pomata and Wei (2021), Nonzero spectral gap in several uniformly spin-2 and hybrid-spin AKLT models: natural kagome cover and the unsuccessful pair-only threshold.",
      "url": "https://doi.org/10.1103/PhysRevResearch.3.013255",
      "doi": "10.1103/PhysRevResearch.3.013255"
    },
    {
      "citation": "Pomata and Wei (2020), Demonstrating the AKLT spectral gap on 2D degree-3 lattices: projector-compression antecedent.",
      "url": "https://doi.org/10.1103/PhysRevLett.124.177203",
      "doi": "10.1103/PhysRevLett.124.177203"
    },
    {
      "citation": "Lemm, Sandvik and Wang (2020), Existence of a spectral gap in the AKLT model on the hexagonal lattice: weighted finite-size and DMRG precedent for a different model.",
      "url": "https://doi.org/10.1103/PhysRevLett.124.177204",
      "doi": "10.1103/PhysRevLett.124.177204"
    },
    {
      "citation": "Rai et al. (2026), A hierarchy of spectral gap certificates for frustration-free spin systems: broader local-positivity methodology.",
      "url": "https://doi.org/10.22331/q-2026-04-13-2065",
      "doi": "10.22331/q-2026-04-13-2065"
    },
    {
      "citation": "Rump (2011), Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse: residual-based numerical verification.",
      "url": "https://doi.org/10.1007/s10543-010-0294-0",
      "doi": "10.1007/s10543-010-0294-0"
    }
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