{
  "model": "Hubbard",
  "lattice": "rectangular-12x16",
  "n_sites": 192,
  "boundary": "P",
  "params": {
    "Nf": 84,
    "U": 8
  },
  "instance_id": "Hubbard/rectangular-12x16_192_P_84_8",
  "rows": [
    {
      "energy": -145.1904,
      "sigma": null,
      "energy_variance": null,
      "dof": 168,
      "einf": 294,
      "v_score": null,
      "method": "Transformer backflow",
      "method_detail": "MARCH",
      "method_as_published": "Transformer backflow + MARCH optimizer",
      "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": "Gu et al., Solving the Hubbard model with neural quantum states, Nat. Commun. 17, 7838 (2026), arXiv:2507.02644, doi:10.1038/s41467-026-74028-6",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2507.02644 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": "−0.7562",
        "note": "Supplementary Table 5, row 16 × 12, t' = 0; dl/gu-si.txt line 190; no error bar | Energy per site in units of t. PBC per the Supplementary Table 5 caption ('Raw data for the energies of Hubbard model under PBC'); U = 8 and hole doping 1/8 per the main text (Fig. 4 caption: 'U = 8 and hole doping δ = 1/8 under PBC'; the t' = -0.2 study: 'Lx × 8 with Lx ranging from 8 to 32, with t' = -0.2 and δ = 1/8'). H has -t' sum_<<ij>>, so t2 = t'. The 16 x 4 and 16 x 16 values at t' = 0 equal the arXiv text's -0.76298 and -0.75630 to the printed digits. No error bar printed. Version read: journal Supplementary Information (41467_2026_74028_MOESM1_ESM.pdf); the arXiv text has no raw-data table.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/rectangular-12x16_192_P_84_8/",
  "per_site_divisor": 192,
  "per_site_label": "E/site",
  "record": {
    "energy": -145.1904,
    "sigma": null,
    "method": "Transformer backflow",
    "method_detail": "MARCH",
    "reference": "Gu et al., Solving the Hubbard model with neural quantum states, Nat. Commun. 17, 7838 (2026), arXiv:2507.02644, doi:10.1038/s41467-026-74028-6",
    "bound_type": "variational",
    "energy_per_site": -0.7562000000000001
  },
  "no_record_reason": null
}