{
  "model": "J1J2",
  "lattice": "square",
  "n_sites": 36,
  "boundary": "P",
  "params": {
    "J2": 0.2
  },
  "instance_id": "J1J2/square_36_P_0.2",
  "rows": [
    {
      "energy": -86.262336,
      "sigma": null,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "ViT",
      "method_detail": "",
      "method_as_published": "ViT",
      "family": "transformer / ViT",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Extremely slow scaling of minimal Hamming distance in quantum sampling data, arXiv:2606.04558",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:2606.04558 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-0.599044",
        "note": "Table I, row J2=0.20, column '6×6, ViT (this work)' | Table I prints energy per site in S.S units: its J2 = 0 QMC column equals Sandvik's exact values on Heisenberg/square_64_P and square_100_P.",
        "secondary_of": null
      },
      "compute": {
        "parameters": null,
        "gpu_hours": null,
        "device": null,
        "n_devices": null,
        "samples": 4096,
        "wall_clock": null,
        "reported_as": "\"The corresponding number of samples is\" ... \"4096.\"",
        "source": "arXiv:2606.04558, located by string match in the committed source text"
      }
    },
    {
      "energy": -86.2488,
      "sigma": 0.00144,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "CNN",
      "method_detail": "",
      "method_as_published": "CNN",
      "family": "CNN / ResNet",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Choo, Neupert & Carleo, Two-dimensional frustrated J1-J2 model studied with neural network quantum states, Phys. Rev. B 100, 125124 (2019)",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "secondary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:2206.14307 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-0.59895(1)",
        "note": "Table 5, row 'Energy(CNN)', 6x6 J2 = 0.2 | Energy per site E/N in S.S units (table captions); the 6x6 exact column equals the exact rows QMBL carries.",
        "secondary_of": "arXiv:2206.14307"
      }
    },
    {
      "energy": -86.262336,
      "sigma": 0.000432,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "RBM",
      "method_detail": "",
      "method_as_published": "RBM wave function",
      "family": "RBM",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Chen, Hendry, Weinberg & Feiguin, Systematic improvement of neural network quantum states using a Lanczos recursion, arXiv:2206.14307 (2022)",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:2206.14307 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-0. 599044(3)",
        "note": "Table 5, row 'Energy(RBM)', 6x6 J2 = 0.2 | Energy per site E/N in S.S units (table captions); the 6x6 exact column equals the exact rows QMBL carries.",
        "secondary_of": null
      }
    },
    {
      "energy": -86.262624,
      "sigma": null,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "ED",
      "method_detail": "",
      "method_as_published": "Exact diagonalization",
      "family": "other",
      "bound_type": "exact",
      "bound_type_reason": "numerically exact reference as stated by the source (assigned during source reading)",
      "reference": "Schulz, Ziman & Poilblanc, Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions, J. Phys. I France 6, 675 (1996), arXiv:cond-mat/9402061",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:cond-mat/9402061 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-0.599046",
        "note": "Table II, row J2 = 0.20, column 36(A1). QMBL's Lanczos (qmbl-runs/qmbl-ed-2026-09-28: E2's ed_sym.py, C4v one-dimensional sectors with even spin at k = 0 (A1, B1)) gives -0.599046322 per site, so the printed value is the correctly rounded ground-state energy. Golubev et al. (arXiv:2606.04558 Table I, 6x6 ED) print -0.599046, also correctly rounded | Ground-state energy per site, J1 = 1, S.S units; the same column reproduces QMBL's exact 36-site rows at J2 = 0, 0.3, 0.4, 0.5, 0.6 to 1e-6.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/J1J2/square_36_P_0.2/",
  "per_site_divisor": 144,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -86.262624,
    "sigma": null,
    "method": "ED",
    "method_detail": "",
    "reference": "Schulz, Ziman & Poilblanc, Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions, J. Phys. I France 6, 675 (1996), arXiv:cond-mat/9402061",
    "bound_type": "exact",
    "energy_per_site": -0.599046
  },
  "no_record_reason": null
}