{
  "model": "J1J2",
  "lattice": "square",
  "n_sites": 36,
  "boundary": "P",
  "params": {
    "J2": 0.6
  },
  "instance_id": "J1J2/square_36_P_0.6",
  "rows": [
    {
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      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "Exact diagonalization",
      "bound_type": "exact",
      "bound_type_reason": "exact diagonalization|ex",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/J1J2/square_36_P_0.6/ed_lattice_symmetries.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
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      "energy_variance": 0.27765980796630174,
      "dof": 36,
      "einf": 0,
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      "method": "DMRG (bond dimension = 2048)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/J1J2/square_36_P_0.6/dmrg.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
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      "method": "RBM (alpha = 1)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/J1J2/square_36_P_0.6/vmc_rbm.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -68.2285,
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      "energy_variance": 42.6698,
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      "einf": 0,
      "v_score": 0.32998291990276646,
      "method": "Jastrow baseline",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/J1J2/square_36_P_0.6/vmc_jastrow.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
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    {
      "energy": -71.01792,
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      "energy_variance": null,
      "dof": 36,
      "einf": 0,
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      "method": "RBM wave function + 2-step Lanczos recursion",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz, or a Lanczos improvement of one (RULES.md 4)",
      "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-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": "-0.49318 (+/- 0.00005) per site in S.S units",
        "note": "Read from Table 2 of arXiv:2206.14307 (J1-J2 on the 6x6 square lattice, PBC, E/N in S.S units), extracted from the PDF with pypdf. p is the number of Lanczos steps. New record for this instance; the exact row is -0.4932386, so it sits 5.9e-5 above the ground state.",
        "secondary_of": null
      }
    },
    {
      "energy": -71.01072,
      "sigma": 0.0072,
      "energy_variance": null,
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      "einf": 0,
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      "method": "RBM wave function + 1-step Lanczos recursion",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz, or a Lanczos improvement of one (RULES.md 4)",
      "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-pdf-2026-09-14",
      "provenance": "primary",
      "verified": {
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        "method": "arXiv PDF text extracted locally with pypdf, no LLM transcription",
        "reported_as": "-0.49313 (+/- 0.00005) per site in S.S units",
        "note": "Read from Table 2 of arXiv:2206.14307 (J1-J2 on the 6x6 square lattice, PBC, E/N in S.S units), extracted from the PDF with pypdf. p is the number of Lanczos steps.",
        "secondary_of": null
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    },
    {
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      "sigma": 0.0072,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "RBM wave function",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz, or a Lanczos improvement of one (RULES.md 4)",
      "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-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": "-0.49298 (+/- 0.00005) per site in S.S units",
        "note": "Read from Table 2 of arXiv:2206.14307 (J1-J2 on the 6x6 square lattice, PBC, E/N in S.S units), extracted from the PDF with pypdf. p is the number of Lanczos steps.",
        "secondary_of": null
      }
    },
    {
      "energy": -70.59312,
      "sigma": 0.00144,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "CNN",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz, or a Lanczos improvement of one (RULES.md 4)",
      "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-pdf-2026-09-14",
      "provenance": "secondary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "arXiv PDF text extracted locally with pypdf, no LLM transcription",
        "reported_as": "-0.49023 (+/- 0.00001) per site in S.S units",
        "note": "Read from Table 2 of arXiv:2206.14307 (J1-J2 on the 6x6 square lattice, PBC, E/N in S.S units), extracted from the PDF with pypdf. p is the number of Lanczos steps.",
        "secondary_of": "Chen, Hendry, Weinberg & Feiguin, Systematic improvement of neural network quantum states using a Lanczos recursion, arXiv:2206.14307 (2022)"
      }
    }
  ],
  "url": "https://qmbl.org/i/J1J2/square_36_P_0.6/",
  "per_site_divisor": 144,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -71.01792,
    "sigma": 0.0072,
    "method": "RBM wave function + 2-step Lanczos recursion",
    "reference": "Chen, Hendry, Weinberg & Feiguin, Systematic improvement of neural network quantum states using a Lanczos recursion, arXiv:2206.14307 (2022)",
    "energy_per_site": -0.49318
  },
  "no_record_reason": null
}