{
  "model": "Hubbard",
  "lattice": "square",
  "n_sites": 64,
  "boundary": "P",
  "params": {
    "Nf": 28,
    "U": -2
  },
  "instance_id": "Hubbard/square_64_P_28_-2",
  "rows": [
    {
      "energy": -130.1568,
      "sigma": null,
      "energy_variance": null,
      "dof": 56,
      "einf": -24.5,
      "v_score": null,
      "method": "SCALE",
      "method_detail": "1 conv layer",
      "method_as_published": "SCALE (1 conv layer), no symmetry projection",
      "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": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2604.25775 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": "-2.0337",
        "note": "Table IV (App. D, attractive Hubbard, t'=0, delta=1/8, PBC); columns 8x8 U=-2 | 8x8 U=-8 | 12x12 U=-2 | 12x12 U=-8; row SCALE, column 8x8 U=-2; sources/2604.25775.txt line 760; version read: arXiv v1 (sources/2604.25775.txt); APS copy not reached (403, 2026-10-16) | Eq. (8): H = -t sum_<ij> - t' sum_<<ij>> + U sum n_up n_dn, t = 1, U = 8, doping 1/8 (Sec. III), periodic unless the column says OBC; energies per site. Pinning fields only in pre-training (App. C).",
        "secondary_of": null
      }
    },
    {
      "energy": -130.1632,
      "sigma": null,
      "energy_variance": null,
      "dof": 56,
      "einf": -24.5,
      "v_score": null,
      "method": "Fixed-node GFMC",
      "method_detail": "trial state: SCALE, 1 conv layer",
      "method_as_published": "SCALE (1 conv layer) trial state + fixed-node GFMC",
      "family": "AFQMC / GFMC",
      "bound_type": "projected",
      "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)",
      "reference": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2604.25775 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": "-2.0338",
        "note": "Table IV (App. D, attractive Hubbard, t'=0, delta=1/8, PBC); columns 8x8 U=-2 | 8x8 U=-8 | 12x12 U=-2 | 12x12 U=-8; row SCALE+GFMC, column 8x8 U=-2; sources/2604.25775.txt line 761; version read: arXiv v1 (sources/2604.25775.txt); APS copy not reached (403, 2026-10-16) | Eq. (8): H = -t sum_<ij> - t' sum_<<ij>> + U sum n_up n_dn, t = 1, U = 8, doping 1/8 (Sec. III), periodic unless the column says OBC; energies per site. Pinning fields only in pre-training (App. C).",
        "secondary_of": null
      }
    },
    {
      "energy": -130.1632,
      "sigma": null,
      "energy_variance": null,
      "dof": 56,
      "einf": -24.5,
      "v_score": null,
      "method": "ACE",
      "method_detail": "16 conv layers",
      "method_as_published": "ACE (16 conv layers), no symmetry projection",
      "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": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2604.25775 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": "-2.0338",
        "note": "Table IV (App. D, attractive Hubbard, t'=0, delta=1/8, PBC); columns 8x8 U=-2 | 8x8 U=-8 | 12x12 U=-2 | 12x12 U=-8; row ACE, column 8x8 U=-2; sources/2604.25775.txt line 762; version read: arXiv v1 (sources/2604.25775.txt); APS copy not reached (403, 2026-10-16) | Eq. (8): H = -t sum_<ij> - t' sum_<<ij>> + U sum n_up n_dn, t = 1, U = 8, doping 1/8 (Sec. III), periodic unless the column says OBC; energies per site. Pinning fields only in pre-training (App. C).",
        "secondary_of": null
      }
    },
    {
      "energy": -130.1696,
      "sigma": null,
      "energy_variance": null,
      "dof": 56,
      "einf": -24.5,
      "v_score": null,
      "method": "Fixed-node GFMC",
      "method_detail": "trial state: ACE",
      "method_as_published": "ACE+GFMC (GFMC projection on the ACE trial state)",
      "family": "AFQMC / GFMC",
      "bound_type": "projected",
      "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)",
      "reference": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2604.25775 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": "-2.0339",
        "note": "Table IV (App. D, attractive Hubbard, t'=0, delta=1/8, PBC); columns 8x8 U=-2 | 8x8 U=-8 | 12x12 U=-2 | 12x12 U=-8; row ACE+GFMC, column 8x8 U=-2; sources/2604.25775.txt line 763; version read: arXiv v1 (sources/2604.25775.txt); APS copy not reached (403, 2026-10-16) | Eq. (8): H = -t sum_<ij> - t' sum_<<ij>> + U sum n_up n_dn, t = 1, U = 8, doping 1/8 (Sec. III), periodic unless the column says OBC; energies per site. Pinning fields only in pre-training (App. C).",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/square_64_P_28_-2/",
  "per_site_divisor": 64,
  "per_site_label": "E/site",
  "record": {
    "energy": -130.1696,
    "sigma": null,
    "method": "Fixed-node GFMC",
    "method_detail": "trial state: ACE",
    "reference": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q",
    "bound_type": "projected",
    "energy_per_site": -2.0339
  },
  "no_record_reason": null
}