{
  "model": "tJ",
  "lattice": "square",
  "n_sites": 32,
  "boundary": "P",
  "params": {
    "t": 1,
    "J": 0.3,
    "t2": 0.3,
    "t3": -0.2,
    "N_up": 15,
    "N_dn": 15,
    "nn_term": true
  },
  "cluster": "square-shaped periodic cluster of 32 sites, edge vectors (4, 4) and (4, -4) (RULES.md 2.1); the source states 'a square lattice with 32 sites and periodic boundary conditions'",
  "instance_id": "tJ/square_32_P_h2_J0.3_tp0.3_tpp-0.2",
  "rows": [
    {
      "energy": -16.601689053076,
      "sigma": null,
      "energy_variance": null,
      "dof": 30,
      "einf": null,
      "v_score": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "",
      "method_as_published": "exact diagonalization",
      "family": "other",
      "bound_type": "exact",
      "bound_type_reason": "numerically exact reference as stated by the source (assigned during source reading)",
      "reference": "Leung, Charge carrier correlation in the electron-doped t-J model, Phys. Rev. B 73, 075104 (2006), doi:10.1103/PhysRevB.73.075104, arXiv:cond-mat/0508035",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0508035 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": "−16.601689",
        "note": "Table I, E_Nc for Nc = 2 charge carriers of the electron-doped model (t = -1, t' = 0.3, t'' = -0.2, J = 0.3) (line 69); version read: arXiv text (sources/cond-mat-0508035.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 = -sum t_ij (c~+c~ + h.c.) + J sum_nn (S_i.S_j - n_i n_j / 4); the electron-doped model is Eq. (1) with t = -1, t' = 0.3, t'' = -0.2, J = 0.3 in the hole operators of the electron-hole transformation (lines 98-114), Nc charge carriers on 32 sites: a t-J model with 32 - Nc particles and no double occupancy. The cluster is bipartite, so the gauge c_i -> (-1)^i c_i takes t = -1 to t = 1 and leaves t' and t'' (same-sublattice hops): t' = 0.3, t'' = -0.2 in the form -t' sum - t'' sum. Total energies (Table I). Convention check: at half filling the source prints E00 = -11.329720 (Table I caption, sources/cond-mat-0508035.txt line 65); with J = 0.3 and -n_i n_j / 4 on the 64 bonds this is 0.3 (E_S.S - 16), so E_S.S / 32 = -0.6801792, the 32-site Heisenberg energy per site -0.680179 printed by Schulz, Ziman & Poilblanc (arXiv:cond-mat/9402061 Table II, J2 = 0.00, column 32; sources/cond-mat-9402061.txt line 1642). Without the -n_i n_j / 4 term E00 would be -6.53.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0508035v1 and v2 PDFs (sources/cond-mat-0508035v{1,2}.pdf; v2 byte-identical to the repo copy), pypdf layout mode, read 2026-10-24; 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, row Nc = 2 (k = (0, 0), d_x2−y2, NB = 150,295,402); identical in v1 and v2",
          "reported_as": "−16.601689 (E_Nc total, units of |t|)",
          "conversion": "none: total energy, |t| = 1; stored -16.601689",
          "note": "Eq. (1) H = -sum_<ij> t_ij (c+c + c+c) + J sum_nn (S_i.S_j - 1/4 n_i n_j), J = 0.3; 'by electron-doped model we mean (1) with hopping parameters t = -1, t' = 0.3, and t'' = -0.2'; t_ij = t, t', t'' at distances 1, sqrt2, 2; 32-site square lattice with periodic boundary conditions. RULES 2.1: on the bipartite 32-site cluster the gauge takes t = -1 to t = 1 and leaves t', t'' (same sublattice): instance t2 = 0.3, t3 = -0.2; Nc carriers = instance holes (32 - Nc spin objects). Internal checks: E00 = -11.329720 = 0.3 (E_S.S - 16) gives -0.680179 per site (the 32-site Heisenberg value), so the -n n/4 term and one count per bond hold; Table II E(pi,0) = -2.583895 gives E1 = E00 + E = -13.913615 (printed -13.913616); Eq. (5) binding energies E2I = -0.1042 and E4I = 1.2037 are reproduced from Table I (-0.104177, 1.203657). Independent exact recompute of this run (out/tjE-exact-recompute) reproduces h1 (-13.9136156041) and h2 (-16.6016890531) in the printed ground-state sectors; h4 was out of reach there. Table I caption: 'Ground state energies, momenta and point group symmetries of the electron-doped model with Nc charge carriers': the global ground state at Nc = 2; bound_type exact (Lanczos ED) is right; journal version (Phys. Rev. B 73, 075104) not reached: journals.aps.org PDF returned 401 on 2026-10-24; arXiv v1 and v2 both read, Table I identical in both; no duplicate on the instance (the data file holds only this row) | Recomputation: E = -16.6016890531 (t = 1); printed form E_Nc total: -16.601689 vs printed -16.601689; 32-site periodic cluster, edge vectors (4, 4) and (-4, 4); t on 64 nn bonds, t' on 64 (1,1) bonds, t'' on 64 (2,0) bonds; momentum x C4v little-group sectors; lowest of 1 sector(s) computed; the remaining sectors were not computed, so the number is confirmed but not that it is the global ground state, best sector sq32P_h2_J0.3_tp0.3_tpp-0.2_k0-0_pg8+-+--+-+_star1, dim 300535476; 9429 s wall on 16 threads over all sectors; not among the six reproduced by checks/tj-ed-2026-10/; sectors computed: the ground-state sector printed in the source's Table I (k = 0, d_x2-y2 = C4v character + - + - - + - +); the other momenta and the 2D irreps at k = 0 and (pi, pi) were not computed, so the ground-state claim rests on the source",
          "source_entry": "tjP6-tj#9 (qmbl-verify 2026-10-23), tjE-exact-recompute#21 (qmbl-verify 2026-10-23)"
        }
      },
      "corrections": [
        {
          "field": "energy",
          "to": -16.601689053076,
          "reported_as": "-16.601689 (E_Nc total)",
          "location": "Table I, E_Nc for Nc = 2 charge carriers of the electron-doped model (t = -1, t' = 0.3, t'' = -0.2, J = 0.3) (line 69)",
          "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": "-16.601689 (total) = -16.601689 (stored); recomputed -16.601689053076 = -16.60168905308 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; 1 symmetry sector (the source's ground-state sector), lowest sector sq32P_h2_J0.3_tp0.3_tpp-0.2_k0-0_pg8+-+--+-+_star1, dimension 300535476), 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#21 (qmbl-verify 2026-10-23); rule for recomputed exact rows, ruled 2026-10-24",
          "from": -16.601689
        }
      ]
    }
  ],
  "url": "https://qmbl.org/i/tJ/square_32_P_h2_J0.3_tp0.3_tpp-0.2/",
  "per_site_divisor": 32,
  "per_site_label": "E/site",
  "best": {
    "exact": {
      "energy": -16.601689053076,
      "sigma": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "",
      "reference": "Leung, Charge carrier correlation in the electron-doped t-J model, Phys. Rev. B 73, 075104 (2006), doi:10.1103/PhysRevB.73.075104, arXiv:cond-mat/0508035",
      "bound_type": "exact",
      "energy_per_site": -0.518802782908625
    },
    "variational": null,
    "projected": null,
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -16.601689053076,
    "sigma": null,
    "method": "ED",
    "ansatz": null,
    "method_detail": "",
    "reference": "Leung, Charge carrier correlation in the electron-doped t-J model, Phys. Rev. B 73, 075104 (2006), doi:10.1103/PhysRevB.73.075104, arXiv:cond-mat/0508035",
    "bound_type": "exact",
    "energy_per_site": -0.518802782908625
  },
  "no_record_reason": null
}