{
  "model": "Heisenberg",
  "lattice": "kagome-4x4",
  "n_sites": 48,
  "boundary": "P",
  "params": {},
  "instance_id": "Heisenberg/kagome-4x4_48_P",
  "rows": [
    {
      "energy": -84.231148254,
      "sigma": 4e-10,
      "energy_variance": null,
      "dof": 48,
      "einf": 0,
      "v_score": null,
      "method": "Exact Diagonalization",
      "bound_type": "exact",
      "bound_type_reason": "exact diagonalization|ex",
      "reference": "[paper](https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.033309)",
      "source": "varbench@2024-10-22",
      "provenance": "imported"
    },
    {
      "energy": -82.643,
      "sigma": 0.005,
      "energy_variance": 10.6,
      "dof": 48,
      "einf": 0,
      "v_score": 0.07449634312700791,
      "method": "VMC with Dirac spin liquid + Jastrow",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/kagome-4x4_48_P/vmc_gutzwiller.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -84,
      "sigma": 0.04,
      "energy_variance": null,
      "dof": 48,
      "einf": 0,
      "v_score": null,
      "method": "GCNN (6 layers, 6 feature maps), symmetric ansatz",
      "bound_type": "variational",
      "bound_type_reason": "assigned during source verification (RULES.md 4)",
      "reference": "Ðurić, Chung, Yang & Sengupta, Spin-1/2 Kagome Heisenberg Antiferromagnet: Machine Learning Discovery of the Spinon Pair-Density-Wave Ground State, Phys. Rev. X 15, 011047 (2025), arXiv:2401.02866",
      "peer_reviewed": true,
      "source": "sweep-pdf-2026-09-14",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "arXiv PDF text extracted locally with pypdf, no LLM transcription",
        "reported_as": "-0.4375 per site in S.S units",
        "note": "Sec. III: \"R = (E_GCNN - E_ED)/E_ED ~ 0.3% with E_ED = -21.057787063 and E_GCNN = -21.00 +/- 0.01\" on the 48-site (4x4x3) PBC cluster, chi0 sector. Total energy in S.S units; E/N = -0.4375. The instance's existing exact row is -0.4387039, i.e. -21.057787063/48 to 8 digits, which confirms the cluster and the convention. Sampling here is the ergodic spin-exchange update, so the objection in arXiv:2605.28861 does not apply to this size.",
        "secondary_of": null
      }
    },
    {
      "energy": -84.1536,
      "sigma": 0.0384,
      "energy_variance": null,
      "dof": 48,
      "einf": 0,
      "v_score": null,
      "method": "DMRG, truncation-error extrapolated (Torus 4)",
      "bound_type": "extrapolated",
      "bound_type_reason": "assigned during source verification (RULES.md 4)",
      "reference": "Depenbrock, McCulloch & Schollwoeck, Nature of the Spin Liquid Ground State of the S=1/2 Heisenberg Model on the Kagome Lattice, Phys. Rev. Lett. 109, 067201 (2012), arXiv:1205.4858",
      "peer_reviewed": true,
      "source": "sweep-pdf-2026-09-14",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "arXiv PDF text extracted locally with pypdf, no LLM transcription",
        "reported_as": "-0.4383 per site in S.S units",
        "note": "Table I row \"Torus 4 -0.4383(2)\". The paper states energies are \"extrapolated in the truncation error of single-site DMRG\", so this is not a strict variational bound (RULES.md 4). Sits above the exact -0.4387039 on this instance.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Heisenberg/kagome-4x4_48_P/",
  "per_site_divisor": 192,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -84,
    "sigma": 0.04,
    "method": "GCNN (6 layers, 6 feature maps), symmetric ansatz",
    "reference": "Ðurić, Chung, Yang & Sengupta, Spin-1/2 Kagome Heisenberg Antiferromagnet: Machine Learning Discovery of the Spinon Pair-Density-Wave Ground State, Phys. Rev. X 15, 011047 (2025), arXiv:2401.02866",
    "energy_per_site": -0.4375
  },
  "no_record_reason": null
}