{
  "model": "Hubbard",
  "lattice": "rectangular-8x32",
  "n_sites": 256,
  "boundary": "P",
  "params": {
    "Nf": 112,
    "U": 8
  },
  "instance_id": "Hubbard/rectangular-8x32_256_P_112_8",
  "rows": [
    {
      "energy": -192.128,
      "sigma": null,
      "energy_variance": null,
      "dof": 224,
      "einf": 392,
      "v_score": null,
      "method": "Tensor-Backflow (NN backflow, direct optimization, Ep = 0)",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Investigating the Fermi-Hubbard model by the tensor-backflow method, arXiv:2507.01856",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-09-15",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-15",
        "method": "source text of arXiv:2507.01856 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table",
        "reported_as": "-0.7505",
        "note": "Table V of arXiv:2507.01856 (pypdf layout text, line 401), 8x32, t' = 0, NN backflow, column Ep = 0 | n = 0.875, U = 8 (Table V caption); PBC: the 8x16 Ep = 1 value equals Table II's 8x16 PBC row, and Figs. 4 and 8 state the 8x32 lattice is under PBC",
        "secondary_of": null
      }
    },
    {
      "energy": -193.2032,
      "sigma": null,
      "energy_variance": null,
      "dof": 224,
      "einf": 392,
      "v_score": null,
      "method": "Tensor-Backflow + 1 Lanczos step (NN backflow, direct optimization, Ep = 1)",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Investigating the Fermi-Hubbard model by the tensor-backflow method, arXiv:2507.01856",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-09-15",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-15",
        "method": "source text of arXiv:2507.01856 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table",
        "reported_as": "-0.7547",
        "note": "Table V of arXiv:2507.01856 (pypdf layout text, line 401), 8x32, t' = 0, NN backflow, column Ep = 1 | n = 0.875, U = 8 (Table V caption); PBC: the 8x16 Ep = 1 value equals Table II's 8x16 PBC row, and Figs. 4 and 8 state the 8x32 lattice is under PBC",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/rectangular-8x32_256_P_112_8/",
  "per_site_divisor": 256,
  "per_site_label": "E/site",
  "record": null,
  "no_record_reason": "sampled rows carry no error bar"
}