{
  "model": "Heisenberg",
  "lattice": "triangular",
  "n_sites": 36,
  "boundary": "P",
  "params": {},
  "instance_id": "Heisenberg/triangular_36_P",
  "rows": [
    {
      "energy": -80.6937689612426,
      "sigma": null,
      "energy_variance": null,
      "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/Heisenberg/triangular_36_P/ed_lattice_symmetries.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -80.36672248793934,
      "sigma": null,
      "energy_variance": 7.068731007373572,
      "dof": 36,
      "einf": 0,
      "v_score": 0.03939956632528572,
      "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/Heisenberg/triangular_36_P/dmrg.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -70.7915,
      "sigma": 0.0065,
      "energy_variance": 43.4753,
      "dof": 36,
      "einf": 0,
      "v_score": 0.3123078200564932,
      "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/Heisenberg/triangular_36_P/vmc_rbm.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -70.0967,
      "sigma": 0.006,
      "energy_variance": 37.0349,
      "dof": 36,
      "einf": 0,
      "v_score": 0.271342943252293,
      "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/Heisenberg/triangular_36_P/vmc_jastrow.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -80.685072,
      "sigma": 0.000432,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "Group CNN (deep, symmetry-projected)",
      "bound_type": "variational",
      "bound_type_reason": "assigned during source verification (RULES.md 4)",
      "reference": "Roth, Szabo & MacDonald, High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks, arXiv:2211.07749 (2023)",
      "peer_reviewed": null,
      "source": "sweep-tables-2026-09-14",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "found in the citing paper's comparison table, then confirmed in the primary source's own PDF (pypdf); no LLM transcription",
        "reported_as": "-0.560313 (+/- 0.000003) per site in S.S units",
        "note": "Read from Table 5 of arXiv:2505.20406 (TLAHM, L=6 triangular lattice, PBC, E/N in S.S units), parsed from the arXiv HTML. Row \"Group Convolutional Neural Network [32]\" = arXiv:2211.07749. Sits 6.0e-5 ABOVE the exact -0.5603734 already on this instance, as a variational bound must. CONFIRMED IN PRIMARY SOURCE - arXiv:2211.07749, results table: \"J2/J1 N GCNN ... Exact/Interpolated ... 0 36 -0.560313(3) - -0.5603734\" - the GCNN energy at J2/J1 = 0, N = 36, printed beside the exact value.",
        "secondary_of": null,
        "found_via": "Moss, Wiersema, Hibat-Allah, Carrasquilla & Melko, arXiv:2505.20406v3 (2025-10-13)"
      }
    },
    {
      "energy": -80.6544,
      "sigma": 0.0576,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "Lattice Convolutional Network",
      "bound_type": "variational",
      "bound_type_reason": "assigned during source verification (RULES.md 4)",
      "reference": "Fu, Zhang, Zhang, Ling, Xu & Ji, Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems, arXiv:2206.07370 (2022)",
      "peer_reviewed": null,
      "source": "sweep-tables-2026-09-14",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "found in the citing paper's comparison table, then confirmed in the primary source's own PDF (pypdf); no LLM transcription",
        "reported_as": "-0.5601 (+/- 0.0004) per site in S.S units",
        "note": "Read from Table 5 of arXiv:2505.20406 (TLAHM, L=6 triangular lattice, PBC, E/N in S.S units), parsed from the arXiv HTML. Row \"Lattice Convolutional Network [49]\" = arXiv:2206.07370. CONFIRMED IN PRIMARY SOURCE - arXiv:2206.07370, results table: \"Triangular 36 0 - -0.55889 -0.5601(4) -0.5603734\" - the special-kernel LCN energy at J2 = 0 on the 36-site triangular lattice.",
        "secondary_of": null,
        "found_via": "Moss, Wiersema, Hibat-Allah, Carrasquilla & Melko, arXiv:2505.20406v3 (2025-10-13)"
      }
    },
    {
      "energy": -80.52768,
      "sigma": null,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "Group CNN",
      "bound_type": "variational",
      "bound_type_reason": "assigned during source verification (RULES.md 4)",
      "reference": "Roth & MacDonald, Group Convolutional Neural Networks Improve Quantum State Accuracy, arXiv:2104.05085 (2021)",
      "peer_reviewed": null,
      "source": "sweep-tables-2026-09-14",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "found in the citing paper's comparison table, then confirmed in the primary source's own PDF (pypdf); no LLM transcription",
        "reported_as": "-0.55922 per site in S.S units",
        "note": "Read from Table 5 of arXiv:2505.20406 (TLAHM, L=6 triangular lattice, PBC, E/N in S.S units), parsed from the arXiv HTML. Row \"Group Convolutional Neural Network [104]\" = arXiv:2104.05085. No error bar is given in the table, so under RULES.md 6 this sampled row cannot hold a record. CONFIRMED IN PRIMARY SOURCE - arXiv:2104.05085, results table: \"J2 = 0 ... ED [28] -0.5603734 ... G-CNN -0.55922\".",
        "secondary_of": null,
        "found_via": "Moss, Wiersema, Hibat-Allah, Carrasquilla & Melko, arXiv:2505.20406v3 (2025-10-13)"
      }
    },
    {
      "energy": -80.0928,
      "sigma": 0.0288,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "2D RNN wavefunction (iterative retraining, s=4.0, r=0.158)",
      "bound_type": "variational",
      "bound_type_reason": "assigned during source verification (RULES.md 4)",
      "reference": "Moss, Wiersema, Hibat-Allah, Carrasquilla & Melko, arXiv:2505.20406v3 (2025-10-13)",
      "peer_reviewed": false,
      "source": "sweep-tables-2026-09-14",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription",
        "reported_as": "-0.5562 (+/- 0.0002) per site in S.S units",
        "note": "Read from Table 5 of arXiv:2505.20406 (TLAHM, L=6 triangular lattice, PBC, E/N in S.S units), parsed from the arXiv HTML. The citing paper's own result.",
        "secondary_of": null,
        "found_via": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Heisenberg/triangular_36_P/",
  "per_site_divisor": 144,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -80.685072,
    "sigma": 0.000432,
    "method": "Group CNN (deep, symmetry-projected)",
    "reference": "Roth, Szabo & MacDonald, High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks, arXiv:2211.07749 (2023)",
    "energy_per_site": -0.5603130000000001
  },
  "no_record_reason": null
}