{
  "model": "tJ",
  "lattice": "square",
  "n_sites": 64,
  "boundary": "P",
  "params": {
    "t": 1,
    "J": 0.4,
    "N_up": 28,
    "N_dn": 28,
    "nn_term": true
  },
  "cluster": "8 x 8 torus (arXiv:cond-mat/0110460: '8 holes on the 8 x 8 lattice', PBC clusters)",
  "instance_id": "tJ/square_64_P_h8_J0.4",
  "rows": [
    {
      "energy": -42.67008,
      "sigma": 0.00384,
      "energy_variance": null,
      "dof": 56,
      "einf": null,
      "v_score": null,
      "method": "FN-GFMC",
      "ansatz": "Gutzwiller",
      "method_detail": "lattice fixed node; projected BCS + Jastrow, 2 Lanczos steps",
      "method_as_published": "FN+2LS",
      "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": "Sorella, Martins, Becca, Gazza, Capriotti, Parola & Dagotto, Superconductivity in the two-dimensional t-J model, Phys. Rev. Lett. 88, 117002 (2002), doi:10.1103/PhysRevLett.88.117002, arXiv:cond-mat/0110460",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0110460 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-22)",
        "reported_as": "−0.66672(6)",
        "note": "text: 8 holes on the 8 x 8 lattice, J/t = 0.4, energy per site (best variational energy per site (FN+2LS)) (line 154); version read: arXiv text (sources/cond-mat-0110460.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = J sum (S_i.S_j - n_i n_j / 4) - t sum c~+c~ + h.c.; energies per site in units of t ('best variational energy per site', 'E = ... t'), 8 holes on the 8 x 8 PBC cluster, J/t = 0.4.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0110460v1 PDF text (sources/cond-mat-0110460.txt, pypdf layout), read 2026-10-24; journal PDF not reachable (APS 401)",
          "location": "p. 3, right column",
          "reported_as": "our best variational energy per site (FN+2LS) is E=−0.66672(6)t",
          "conversion": "-0.66672 x 64 = -42.67008; sigma 0.00006 x 64 = 0.00384",
          "note": "Fixed node with the 2-Lanczos-step state as guiding function (ten Haaf lattice FN, Ref. 14): projected, correct. Same cluster/sector/couplings as the record row. No duplicate.",
          "source_entry": "tjP7-tj#1 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -42.944,
      "sigma": 0.064,
      "energy_variance": null,
      "dof": 56,
      "einf": null,
      "v_score": null,
      "method": "VMC",
      "ansatz": "Gutzwiller",
      "method_detail": "projected BCS + Jastrow with Lanczos steps; extrapolated: variance → 0",
      "method_as_published": "zero variance extrapolation",
      "family": "classic VMC",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "Sorella, Martins, Becca, Gazza, Capriotti, Parola & Dagotto, Superconductivity in the two-dimensional t-J model, Phys. Rev. Lett. 88, 117002 (2002), doi:10.1103/PhysRevLett.88.117002, arXiv:cond-mat/0110460",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0110460 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-22)",
        "reported_as": "−0.671(1)",
        "note": "text: 8 holes on the 8 x 8 lattice, J/t = 0.4, energy per site (the zero variance extrapolation) (line 156); version read: arXiv text (sources/cond-mat-0110460.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = J sum (S_i.S_j - n_i n_j / 4) - t sum c~+c~ + h.c.; energies per site in units of t ('best variational energy per site', 'E = ... t'), 8 holes on the 8 x 8 PBC cluster, J/t = 0.4.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0110460v1 PDF text (sources/cond-mat-0110460.txt, pypdf layout), read 2026-10-24; journal PDF not reachable (APS 401)",
          "location": "p. 3, right column, paragraph 'For 8 holes on the 8×8 lattice and J/t=0.4'",
          "reported_as": "close to the zero variance extrapolation E=−0.671(1)t",
          "conversion": "-0.671 x 64 = -42.944; sigma 0.001 x 64 = 0.064",
          "note": "Record row. Own computation; PBC 8x8, 8 holes (N_up = N_dn = 28), J/t = 0.4, Eq. (1) is the QMBL form incl. -n n/4; variance extrapolation (Ref. 6) -> extrapolated, correct. Lies 4.3 sigma below the FN+2LS bound; holds the record as an extrapolation under RULES 6. No duplicate on the instance.",
          "source_entry": "tjP7-tj#0 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -41.13024,
      "sigma": 0.00512,
      "energy_variance": null,
      "dof": 56,
      "einf": null,
      "v_score": null,
      "method": "VMC",
      "ansatz": "Gutzwiller",
      "method_detail": "",
      "method_as_published": "VMC",
      "family": "classic VMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Sorella, Martins, Becca, Gazza, Capriotti, Parola & Dagotto, Superconductivity in the two-dimensional t-J model, Phys. Rev. Lett. 88, 117002 (2002), doi:10.1103/PhysRevLett.88.117002, arXiv:cond-mat/0110460",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0110460 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-22)",
        "reported_as": "−0.64266(8)",
        "note": "text: 8 holes on the 8 x 8 lattice, J/t = 0.4, energy per site (the pure variational calculation) (line 157); version read: arXiv text (sources/cond-mat-0110460.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = J sum (S_i.S_j - n_i n_j / 4) - t sum c~+c~ + h.c.; energies per site in units of t ('best variational energy per site', 'E = ... t'), 8 holes on the 8 x 8 PBC cluster, J/t = 0.4.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0110460v1 PDF text (sources/cond-mat-0110460.txt, pypdf layout), read 2026-10-24; journal PDF not reachable (APS 401)",
          "location": "p. 3, right column",
          "reported_as": "much better than the pure variational calculation, E=−0.64266(8)t",
          "conversion": "-0.64266 x 64 = -41.13024; sigma 0.00008 x 64 = 0.00512",
          "note": "Pure VMC of the projected BCS + Jastrow state (Eq. 2): variational, correct. No duplicate.",
          "source_entry": "tjP7-tj#2 (qmbl-verify 2026-10-23)"
        }
      }
    }
  ],
  "url": "https://qmbl.org/i/tJ/square_64_P_h8_J0.4/",
  "per_site_divisor": 64,
  "per_site_label": "E/site",
  "best": {
    "exact": null,
    "variational": {
      "energy": -41.13024,
      "sigma": 0.00512,
      "method": "VMC",
      "ansatz": "Gutzwiller",
      "method_detail": "",
      "reference": "Sorella, Martins, Becca, Gazza, Capriotti, Parola & Dagotto, Superconductivity in the two-dimensional t-J model, Phys. Rev. Lett. 88, 117002 (2002), doi:10.1103/PhysRevLett.88.117002, arXiv:cond-mat/0110460",
      "bound_type": "variational",
      "energy_per_site": -0.64266
    },
    "projected": {
      "energy": -42.67008,
      "sigma": 0.00384,
      "method": "FN-GFMC",
      "ansatz": "Gutzwiller",
      "method_detail": "lattice fixed node; projected BCS + Jastrow, 2 Lanczos steps",
      "reference": "Sorella, Martins, Becca, Gazza, Capriotti, Parola & Dagotto, Superconductivity in the two-dimensional t-J model, Phys. Rev. Lett. 88, 117002 (2002), doi:10.1103/PhysRevLett.88.117002, arXiv:cond-mat/0110460",
      "bound_type": "projected",
      "energy_per_site": -0.66672
    },
    "extrapolated": {
      "energy": -42.944,
      "sigma": 0.064,
      "method": "VMC",
      "ansatz": "Gutzwiller",
      "method_detail": "projected BCS + Jastrow with Lanczos steps; extrapolated: variance → 0",
      "reference": "Sorella, Martins, Becca, Gazza, Capriotti, Parola & Dagotto, Superconductivity in the two-dimensional t-J model, Phys. Rev. Lett. 88, 117002 (2002), doi:10.1103/PhysRevLett.88.117002, arXiv:cond-mat/0110460",
      "bound_type": "extrapolated",
      "energy_per_site": -0.671
    },
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -42.944,
    "sigma": 0.064,
    "method": "VMC",
    "ansatz": "Gutzwiller",
    "method_detail": "projected BCS + Jastrow with Lanczos steps; extrapolated: variance → 0",
    "reference": "Sorella, Martins, Becca, Gazza, Capriotti, Parola & Dagotto, Superconductivity in the two-dimensional t-J model, Phys. Rev. Lett. 88, 117002 (2002), doi:10.1103/PhysRevLett.88.117002, arXiv:cond-mat/0110460",
    "bound_type": "extrapolated",
    "energy_per_site": -0.671
  },
  "no_record_reason": null
}