{
  "model": "Hubbard",
  "lattice": "square",
  "n_sites": 256,
  "boundary": "O",
  "params": {
    "Nf": 112,
    "U": 8,
    "t1": 1,
    "t2": -0.2
  },
  "instance_id": "Hubbard/square_256_O_112_8_t12_-0.2",
  "rows": [
    {
      "energy": -180.4288,
      "sigma": 0.1792,
      "energy_variance": null,
      "dof": 224,
      "einf": 392,
      "v_score": null,
      "method": "Tensor backflow",
      "method_detail": "wave function of the PBC run with pinning field PF3, re-optimised 1324 steps with open boundaries",
      "method_as_published": "Tensor backflow (p = 0, OBC, from the PF3 PBC state, 1324 steps)",
      "family": "backflow / Pfaffian",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2609.22618 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": "-0.7048(7)",
        "note": "Section III.C (OBC) text; sources/2609.22618.txt line 573; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_<ij> - t' sum_<<ij>> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.",
        "secondary_of": null
      }
    },
    {
      "energy": -181.6832,
      "sigma": 0.0256,
      "energy_variance": null,
      "dof": 224,
      "einf": 392,
      "v_score": null,
      "method": "Tensor backflow",
      "method_detail": "wave function of the PBC run with pinning field PF3, re-optimised 1324 steps with open boundaries, 1 Lanczos step",
      "method_as_published": "Tensor backflow (p = 1, OBC, from the PF3 PBC state, 1324 steps)",
      "family": "backflow / Pfaffian",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2609.22618 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": "-0.7097(1)",
        "note": "Section III.C (OBC) text; also Fig. 7 caption; sources/2609.22618.txt line 573; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_<ij> - t' sum_<<ij>> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/square_256_O_112_8_t12_-0.2/",
  "per_site_divisor": 256,
  "per_site_label": "E/site",
  "record": {
    "energy": -181.6832,
    "sigma": 0.0256,
    "method": "Tensor backflow",
    "method_detail": "wave function of the PBC run with pinning field PF3, re-optimised 1324 steps with open boundaries, 1 Lanczos step",
    "reference": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618",
    "bound_type": "variational",
    "energy_per_site": -0.7097
  },
  "no_record_reason": null
}