{
  "model": "J1J2",
  "lattice": "square",
  "n_sites": 100,
  "boundary": "P",
  "params": {
    "J2": 0.5
  },
  "instance_id": "J1J2/square_100_P_0.5",
  "rows": [
    {
      "energy": -198.06,
      "sigma": 0.009,
      "energy_variance": 11.6,
      "dof": 100,
      "einf": 0,
      "v_score": 0.029570892998855538,
      "method": "VMC with projected BCS (Z2 spin liquid)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/J1J2/square_100_P_0.5/vmc_gutzwiller.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -199.05174,
      "sigma": 0.00044,
      "energy_variance": 0.79,
      "dof": 100,
      "einf": 0,
      "v_score": 0.001993862175592732,
      "method": "RBM+PP with momentum (K=0), spin-parity (even S), and point-group (A1) projections, 16 hidden units",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[paper](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.031034)",
      "source": "varbench@2024-10-22",
      "provenance": "imported"
    },
    {
      "energy": -198.157,
      "sigma": 0.003,
      "energy_variance": 1.6237,
      "dof": 100,
      "einf": 0,
      "v_score": 0.004135108919547855,
      "method": "RNN",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/J1J2/square_100_P_0.5/vmc_rnn.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -198.239,
      "sigma": 0.017,
      "energy_variance": 4.671,
      "dof": 100,
      "einf": 0,
      "v_score": 0.011885889016072248,
      "method": "RNN + translational symmetry",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/J1J2/square_100_P_0.5/vmc_rnn.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -196.55931995563643,
      "sigma": null,
      "energy_variance": 16.657353288515882,
      "dof": 100,
      "einf": 0,
      "v_score": 0.04311403947286857,
      "method": "DMRG (bond dimension = 1024)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/J1J2/square_100_P_0.5/dmrg.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -190.8007,
      "sigma": 0.0084,
      "energy_variance": 71.58155,
      "dof": 100,
      "einf": 0,
      "v_score": 0.19662610252811577,
      "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_100_P_0.5/vmc_rbm.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -189.5607,
      "sigma": 0.0084,
      "energy_variance": 71.68267,
      "dof": 100,
      "einf": 0,
      "v_score": 0.199488362664073,
      "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_100_P_0.5/vmc_jastrow.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -199.07684,
      "sigma": 0.00016,
      "energy_variance": null,
      "dof": 100,
      "einf": 0,
      "v_score": null,
      "method": "ResNet2 (64 conv layers, >1e6 params), MinSR",
      "bound_type": "variational",
      "bound_type_reason": "assigned from the source text during verification",
      "reference": "Chen & Heyl, Nat. Phys. 20, 1476 (2024), arXiv:2302.01941",
      "peer_reviewed": true,
      "source": "literature-2025-26",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-10",
        "method": "source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription",
        "reported_as": "-0.4976921 (+/- 4e-7) per site in S.S units",
        "note": "PDF text: \"to attain the best variational energy E/N = -0.4976921(4)\"",
        "secondary_of": null
      }
    },
    {
      "energy": -199.086,
      "sigma": 0.0036,
      "energy_variance": null,
      "dof": 100,
      "einf": 0,
      "v_score": null,
      "method": "ResNet2 MinSR, zero-variance extrapolation",
      "bound_type": "extrapolated",
      "bound_type_reason": "assigned from the source text during verification",
      "reference": "Chen & Heyl, Nat. Phys. 20, 1476 (2024), arXiv:2302.01941",
      "peer_reviewed": true,
      "source": "literature-2025-26",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-10",
        "method": "source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription",
        "reported_as": "-0.497715 (+/- 0.000009) per site in S.S units",
        "note": "PDF text: \"estimate the ground-state energy E_GS/N = -0.497715(9) by zero-variance extrapolation\". NOT a variational bound.",
        "secondary_of": null
      }
    },
    {
      "energy": -199.0536,
      "sigma": 0.0004,
      "energy_variance": null,
      "dof": 100,
      "einf": 0,
      "v_score": null,
      "method": "fViT (vision transformer, 2.7e5 params)",
      "bound_type": "variational",
      "bound_type_reason": "assigned from the source text during verification",
      "reference": "Nutakki, Shokry & Vicentini, Phys. Rev. Research 7, 043099 (2025), arXiv:2505.03466",
      "peer_reviewed": true,
      "source": "literature-2025-26",
      "provenance": "secondary",
      "verified": {
        "checked_on": "2026-09-10",
        "method": "source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription",
        "reported_as": "-0.497634 (+/- 0.000001) per site in S.S units",
        "note": "Read from Table 1 of the arXiv HTML of 2505.03466; primary source not checked.",
        "secondary_of": "Rende et al., cited as ref [16] of arXiv:2505.03466"
      }
    },
    {
      "energy": -199.0332,
      "sigma": 0.0024,
      "energy_variance": null,
      "dof": 100,
      "einf": 0,
      "v_score": null,
      "method": "ConvNext (6,3,3)[2,2], 2.6e5 params",
      "bound_type": "variational",
      "bound_type_reason": "assigned from the source text during verification",
      "reference": "Nutakki, Shokry & Vicentini, Phys. Rev. Research 7, 043099 (2025), arXiv:2505.03466",
      "peer_reviewed": true,
      "source": "literature-2025-26",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-10",
        "method": "source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription",
        "reported_as": "-0.497583 (+/- 0.000006) per site in S.S units",
        "note": "Table 1 of arXiv:2505.03466, their own result. Paper states L=10, PBC, S.S per site.",
        "secondary_of": null
      }
    },
    {
      "energy": -199.07756,
      "sigma": 0.00008,
      "energy_variance": null,
      "dof": 100,
      "einf": 0,
      "v_score": null,
      "method": "CNN-MPS (h,D,l)=(32,20,20), Marshall sign transformation",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz; energy is a strict upper bound (assigned during source verification)",
      "reference": "arXiv:2603.14425, Disentangling Tensor Network States with Deep Neural Networks",
      "peer_reviewed": false,
      "source": "sweep-2026-09-13",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-13",
        "method": "arXiv HTML parsed locally, no LLM transcription",
        "reported_as": "-0.4976939 (+/- 2e-7) per site in S.S units",
        "note": "Read from Table 1 of arXiv:2603.14425 (square-lattice J1-J2 at J2/J1=0.5, PBC, E per site in S.S units), parsed from the arXiv HTML. Claim: \"the best energy obtained by CNN-MPS is -0.4976939(2) ... which is lower than the best previously reported result\". Supersedes Chen & Heyl -0.4976921(4) as the record for this instance.",
        "secondary_of": null
      }
    },
    {
      "energy": -199.07692,
      "sigma": 0.00008,
      "energy_variance": null,
      "dof": 100,
      "einf": 0,
      "v_score": null,
      "method": "T-MPS",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz; energy is a strict upper bound (assigned during source verification)",
      "reference": "arXiv:2603.14425, Disentangling Tensor Network States with Deep Neural Networks",
      "peer_reviewed": false,
      "source": "sweep-2026-09-13",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-13",
        "method": "arXiv HTML parsed locally, no LLM transcription",
        "reported_as": "-0.4976923 (+/- 2e-7) per site in S.S units",
        "note": "Read from Table 1 of arXiv:2603.14425 (square-lattice J1-J2 at J2/J1=0.5, PBC, E per site in S.S units), parsed from the arXiv HTML.",
        "secondary_of": null
      }
    },
    {
      "energy": -199.07056,
      "sigma": 0.00028,
      "energy_variance": null,
      "dof": 100,
      "einf": 0,
      "v_score": null,
      "method": "Convolutional transformer wave function (CTWF)",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz; energy is a strict upper bound (assigned during source verification)",
      "reference": "Chen, Naik & Heyl, Convolutional transformer wave functions, arXiv:2503.10462",
      "peer_reviewed": false,
      "source": "sweep-2026-09-13",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-13",
        "method": "arXiv HTML parsed locally, no LLM transcription",
        "reported_as": "-0.4976764 (+/- 7e-7) per site in S.S units",
        "note": "Read from Table 1 of arXiv:2603.14425 (square-lattice J1-J2 at J2/J1=0.5, PBC, E per site in S.S units), parsed from the arXiv HTML. Cross-checked against the CTWF paper's own text.",
        "secondary_of": null
      }
    },
    {
      "energy": -199.128,
      "sigma": 0.012,
      "energy_variance": null,
      "dof": 100,
      "einf": 0,
      "v_score": null,
      "method": "Holographic Quantum Transformer (HQT), zero-shot 8x8->10x10 transfer",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz; energy is a strict upper bound (assigned during source verification)",
      "reference": "Holographic Quantum Transformer, arXiv:2607.00398 (conference proceedings)",
      "peer_reviewed": true,
      "source": "sweep-2026-09-13",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-13",
        "method": "arXiv HTML parsed locally, no LLM transcription",
        "reported_as": "-0.49782 (+/- 0.00003) per site in S.S units",
        "note": "Abstract: \"This zero-shot protocol yields an energy of E/N = -0.49782(3), statistically consistent with the variational state of the art\". It is not consistent: it is 1.3e-4 BELOW the best variational energy (CNN-MPS -0.4976939(2)) and 1.05e-4 below the zero-variance extrapolated ground state -0.497715(9), i.e. below the ground state itself, which no variational energy can be. See the defect flag.",
        "secondary_of": null
      },
      "defect": {
        "flag": "energy-variance-inconsistent",
        "finding": "Claimed 1.3e-4 below the best variational energy (CNN-MPS) while the paper itself calls the number 'statistically consistent with the variational state of the art' - it is lower by ~4x its own stated error bar, so if real it is an unclaimed record. There is NO exact reference at 10x10 (ED reaches ~6x6 for this model), so this is a contested record claim, not a proven error.",
        "diagnosis": "The reported energy is inconsistent with the paper's OWN reported variance. At 8x8 the claimed E/N = -0.5001 beats RBM+PP's -0.4989635 while the reported variance (sigma^2 = 1.4e-3 per site, S.S units) gives a V-score of 5.6e-3 against RBM+PP's 9.81e-4 - 5.7x worse. Energy and variance move together - a state further from an eigenstate cannot be lower in energy - so by the V-score calibration this energy should be ~1.2e-3 higher than claimed.",
        "ruled_out": "NOT 'below the exact ground state'. There is no exact reference at 8x8 or 10x10: ED for this model reaches about 6x6, and the paper correctly uses 6x6 ED (-0.5038) as its only exact anchor. Chen & Heyl's -0.497715(9) is a zero-variance extrapolation, not a bound, so a lower variational energy would only mean the extrapolation carries systematic error. The sigma^2 is per site, so the V-score is 5.6e-3 and not a range. Separately, the paper is internally inconsistent about it: Table 1 gives sigma^2 = 1.4e-3 for the 8x8 run while the J2 scan lists 0.0034 at J2 = 0.50, which would make the V-score 1.4e-2 and the contradiction larger. No variance is reported at 10x10 at all, so that row's flag rests only on it being an unclaimed record.",
        "evidence": "arXiv:2607.00398 Tables 1-3; V-scores recomputed from this instance's own rows."
      }
    }
  ],
  "url": "https://qmbl.org/i/J1J2/square_100_P_0.5/",
  "per_site_divisor": 400,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -199.07756,
    "sigma": 0.00008,
    "method": "CNN-MPS (h,D,l)=(32,20,20), Marshall sign transformation",
    "reference": "arXiv:2603.14425, Disentangling Tensor Network States with Deep Neural Networks",
    "energy_per_site": -0.4976939
  },
  "no_record_reason": null
}