{
  "model": "tJ",
  "lattice": "ladder-3x6",
  "n_sites": 18,
  "boundary": "A",
  "params": {
    "t": 1,
    "J": 0.5,
    "N_up": 9,
    "N_dn": 8,
    "nn_term": true
  },
  "cluster": "three-leg ladder of 6 rungs, isotropic (t' = t, J' = J on the rungs), antiperiodic along the legs and open across them (arXiv:cond-mat/9706147 Table I); QMBL's diagonalization reproduces both energies (checks/tj-ed-2026-10/)",
  "instance_id": "tJ/ladder-3x6_18_A_h1_J0.5",
  "rows": [
    {
      "energy": -10.407574528812,
      "sigma": null,
      "energy_variance": null,
      "dof": 17,
      "einf": null,
      "v_score": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "Lanczos",
      "method_as_published": "Lanczos",
      "family": "other",
      "bound_type": "exact",
      "bound_type_reason": "numerically exact reference as stated by the source (assigned during source reading)",
      "reference": "Rice, Haas, Sigrist & Zhang, Lightly doped t-J three-leg ladders: An analog for the underdoped cuprates, Phys. Rev. B 56, 14655 (1997), doi:10.1103/PhysRevB.56.14655, arXiv:cond-mat/9706147",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/9706147 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": "-10.40757",
        "note": "Table I, 3 x 6 isotropic ladder, 1 hole, lowest entry of the column (k = π/2, R = -1) (line 609); version read: arXiv text (sources/cond-mat-9706147.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 = -t sum P(c+c + h.c.)P - t' sum (rungs) + J sum (S.S - n n / 4) + J' sum (rungs), isotropic t' = t, J' = J, J/t = 0.5; Table I prints total energies per symmetry sector; the lowest of each column is the ground state, and QMBL's diagonalization of the 3 x 6 ladder with antiperiodic legs gives -10.4075745288 (1 hole) and -11.8068024851 (2 holes).",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/9706147v2 PDF, pypdf layout (sources/tjP7-dl/cond-mat-9706147v2.layout.txt); journal PDF not reachable (APS 401); and an independent recomputation: independent exact diagonalization written for this check (checks/tj-exact-recompute-2026-10/tjk.c: C/OpenMP, basis adapted to lattice translations and point-group operations with 1D characters, Lanczos to |dE| < 1e-13 per step; clusters and sectors from gen.py), run 2026-10-23; validated against a brute-force full-space ED (bf.py) on 12 small clusters (agreement to 1e-10)",
          "location": "Table I, 1-hole column, row k = π/2, R = -1",
          "reported_as": "-10.40757",
          "conversion": "total, no conversion",
          "note": "Lowest of the six 1-hole sector entries (others -10.24582, -10.25131, -10.25673, -9.987594, -10.18534); k = ±π/6, ±π/2, ±5π/6 exhaust the APBC momenta. APBC legs, open rungs, isotropic J/t = 0.5, Eq. (1) has -n n/4. QMBL ED -10.4075745288 agrees. No duplicate. | Recomputation: E = -10.4075745288 (t = 1); printed form total, units of t: -10.40757 vs printed -10.40757; 3 x 6 ladder (three legs of 6 sites), hopping across the leg boundary with the opposite sign (antiperiodic legs), open across, isotropic; full space, no symmetry; full space at this electron number (ground state), best sector lad3x6A_h1_J0.5_full, dim 437580; 2 s wall on 16 threads over all sectors; QMBL's earlier ED (checks/tj-ed-2026-10/) gave -10.4075745288, difference -1.2e-11",
          "source_entry": "tjP7-tj#5 (qmbl-verify 2026-10-23), tjE-exact-recompute#4 (qmbl-verify 2026-10-23)"
        }
      },
      "corrections": [
        {
          "field": "energy",
          "to": -10.407574528812,
          "reported_as": "-10.40757 (total, units of t)",
          "location": "Table I, 3 x 6 isotropic ladder, 1 hole, lowest entry of the column (k = π/2, R = -1) (line 609)",
          "version_read": "recomputation: checks/tj-exact-recompute-2026-10/ (tjk.c, 2026-10-23); the printed value as the generator read it (scripts/tj_2026_10_22.mjs)",
          "conversion": "-10.40757 (total) = -10.40757 (stored); recomputed -10.407574528812 = -10.4075745288 in the printed form, which rounds to the printed digits",
          "checked_on": "2026-10-23",
          "reason": "Rule for exact rows QMBL recomputed (2026-09-30; applied to the t-J rows, ruled 2026-10-24): the printed value is QMBL's value rounded to the printed digits, so the row keeps its citation and carries QMBL's digits; the printed value stays here. Recomputed by tjk.c (symmetry-adapted Lanczos, |dE| < 1e-13 per step; the full space at its electron number, lowest sector lad3x6A_h1_J0.5_full, dimension 437580), whose code agrees with the brute-force bf.py to 1e-10 on 12 small clusters; codes and outputs in checks/tj-exact-recompute-2026-10/.",
          "source_entry": "tjE-exact-recompute#4 (qmbl-verify 2026-10-23); rule for recomputed exact rows, ruled 2026-10-24",
          "from": -10.40757
        },
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-10.40757",
          "location": "Table I, 3 x 6 isotropic ladder, 1 hole, lowest entry of the column (k = π/2, R = -1) (line 609)",
          "version_read": "the row's published method string; the exact diagonalization is recomputed in checks/tj-exact-recompute-2026-10/",
          "conversion": "none",
          "checked_on": "2026-10-24",
          "reason": "Deterministic: an exact (Lanczos) diagonalization carries no statistical error, but the label \"Lanczos\" matches none of isSampled's deterministic markers, so the row read as a sampled energy without an error bar (the README marked it); ruled 2026-10-24.",
          "source_entry": "tjE-exact-recompute#4 (qmbl-verify 2026-10-23); ruled 2026-10-24 (exact rows whose label reads as sampled)",
          "from": true
        }
      ],
      "sampled": false
    }
  ],
  "url": "https://qmbl.org/i/tJ/ladder-3x6_18_A_h1_J0.5/",
  "per_site_divisor": 18,
  "per_site_label": "E/site",
  "best": {
    "exact": {
      "energy": -10.407574528812,
      "sigma": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "Lanczos",
      "reference": "Rice, Haas, Sigrist & Zhang, Lightly doped t-J three-leg ladders: An analog for the underdoped cuprates, Phys. Rev. B 56, 14655 (1997), doi:10.1103/PhysRevB.56.14655, arXiv:cond-mat/9706147",
      "bound_type": "exact",
      "energy_per_site": -0.578198584934
    },
    "variational": null,
    "projected": null,
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -10.407574528812,
    "sigma": null,
    "method": "ED",
    "ansatz": null,
    "method_detail": "Lanczos",
    "reference": "Rice, Haas, Sigrist & Zhang, Lightly doped t-J three-leg ladders: An analog for the underdoped cuprates, Phys. Rev. B 56, 14655 (1997), doi:10.1103/PhysRevB.56.14655, arXiv:cond-mat/9706147",
    "bound_type": "exact",
    "energy_per_site": -0.578198584934
  },
  "no_record_reason": null
}