{
  "model": "tJ",
  "lattice": "square",
  "n_sites": 26,
  "boundary": "P",
  "params": {
    "t": 1,
    "J": 0.3,
    "N_up": 11,
    "N_dn": 11,
    "nn_term": true
  },
  "cluster": "square-shaped periodic cluster of 26 sites, edge vectors (5, 1) and (-1, 5), the only square-shaped cluster with N = 26 (RULES.md 2.1). Inferred, not printed: arXiv:cond-mat/0606659 describes its clusters as 'a square lattice with L sites and periodic boundary conditions rotated by 45 degrees such that L = 2l^2, l being an odd integer', which does not include L = 26, and states no other shape; arXiv:cond-mat/0009149 lists 13 shells for its 26-site cluster, as the (5, 1) cluster has (SWEEP.md, 2026-10-22). Confirmed by QMBL's diagonalization of the (5, 1) cluster (checks/tj-exact-recompute-2026-10/, 2026-10-23), which reproduces every printed 26-site exact energy to its printed digits: with 2 holes in all 14 momentum and C4 sectors, with 4 holes in the zero-momentum, C4-even sector, the lowest of the 1 to 6 of 14 sectors computed",
  "instance_id": "tJ/square_26_P_h4_J0.3",
  "rows": [
    {
      "energy": -16.708026076752,
      "sigma": null,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "",
      "method_as_published": "Exact (D. Poilblanc, unpublished)",
      "family": "other",
      "bound_type": "exact",
      "bound_type_reason": "numerically exact reference as stated by the source (assigned during source reading)",
      "reference": "D. Poilblanc, unpublished exact diagonalization data on the 26-site t-J model, printed in Sorella, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), Table I, doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149 (acknowledgements)",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "secondary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0009149 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": "-0.64262",
        "note": "Table I, N = 22, L = 26, J/t = 0.3, column Exact; the acknowledgements (lines 829-831) credit D. Poilblanc's unpublished 26-site data (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.",
        "secondary_of": "arXiv:cond-mat/0009149",
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0009149v1 PDF, pypdf layout mode (table row parsed by out/tjP2-10-1103-physrevb-64-024512/build.py); 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 (page 17), row N = 22, L = 26, J/t = 0.3, column Exact (layout text line 1050; header line 1049)",
          "reported_as": "-0.64262 per site, t = 1",
          "conversion": "-0.64262 x 26 = -16.70812; no error bar printed (exact column)",
          "note": "Exact column of Table I. Provenance: the paper's text says 'the largest size cases where the exact solution is known 4 holes in 26 sites 23' (ref. 23 = D. Poilblanc, Phys. Rev. B 52, 9201 (1995)) and the acknowledgements say 'D. Poilblanc and P. W. Leung who kindly sent me unpublished data on the 26 and 32 site t-J model, respectively'. Poilblanc 1995 (arXiv v1 read) shows 26-site 4-hole energies only in Fig. 3 (no table, no printed digits found by grep), so the stored 'unpublished, printed in Sorella' secondary attribution with peer_reviewed true follows RULES.md 8 (private communication printed in a paper). Suggestion, not a correction: the method reference could add Poilblanc PRB 52, 9201 (1995), which states the Hamiltonian and cluster that tj_2026_10_22.mjs line 71 currently infers from Lugas et al. Stored total is the printed 5-decimal per-site value x 26; the full-precision ED of this run (tjE-exact-recompute) gives a total that rounds to the same per-site digits. No duplicate on the instance: Lugas et al. Table II prints the same Eex/L but carries no row on this instance. bound_type exact agrees (Lanczos ED). N = 22 electrons on L = 26 sites = 4 holes, N_up = N_dn = 11 (singlet); t = 1 and J/t from the row; energy per site, converted to total by x 26; sigma (1) in the last printed digit = 1e-4 per site (caption: 'statistical accuracy of 10^-4 t on the energy per site'). Hamiltonian not printed in this paper; the convention J(S.S - n n/4) and the sqrt(26) x sqrt(26) periodic cluster are fixed by the paper's ref. 23 (Poilblanc, PRB 52, 9201 (1995), arXiv:cond-mat/9505004v1, which prints H = t sum c+c + J sum (S.S - n n/4) on sqrt(N) x sqrt(N) clusters and footnote 17 '22 electrons on 26 sites'), by the exact column being reproduced on the (5, 1) cluster with that Hamiltonian (out/tjE-exact-recompute, this run), and by Lugas et al. PRB 74, 165122 Table II printing the same exact column. arXiv:cond-mat/0009149v1 (only arXiv version, 11 Sep 2000), PDF text by pypdf layout and plain mode (sources/tjP2-dl/cond-mat-0009149v1.layout.txt); journal version Phys. Rev. B 64, 024512 (2001) not reached: the APS PDF returned HTTP 401 from this session on 2026-10-24 (abstract page only: received 12 Sep 2000, published 19 Jun 2001). | Recomputation: E = -16.7080260768 (t = 1); printed form E/L: -0.64262 vs printed -0.64262; 26-site square-shaped periodic cluster, edge vectors (5, 1) and (-1, 5) (52 bonds); 14 sectors in all: Gamma and M with the four C4 characters, six C4 stars of 4 momenta with translations only; lowest of 6 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 sq26P_h4_J0.3_k0-0_l0_star1, dim 101410008; 21929 s wall on 16 threads over all sectors; not among the six reproduced by checks/tj-ed-2026-10/; the computed energy on the (5, 1) cluster reproduces the printed value, which confirms the inferred cluster shape; the lowest sector is Gamma with C4 eigenvalue +1 (l = 0)",
          "source_entry": "tjP2-10-1103-physrevb-64-024512#0 (qmbl-verify 2026-10-23), tjE-exact-recompute#14 (qmbl-verify 2026-10-23)"
        }
      },
      "corrections": [
        {
          "field": "energy",
          "to": -16.708026076752,
          "reported_as": "-0.64262 (E/L)",
          "location": "Table I, N = 22, L = 26, J/t = 0.3, column Exact",
          "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": "-0.64262 x 26 = -16.70812 (stored); recomputed -16.708026076752 = -0.6426163876 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; 6 of 14 symmetry sectors, lowest sector sq26P_h4_J0.3_k0-0_l0_star1, dimension 101410008), 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#14 (qmbl-verify 2026-10-23); rule for recomputed exact rows, ruled 2026-10-24",
          "from": -16.70812
        },
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-0.64262",
          "location": "Table I, N = 22, L = 26, J/t = 0.3, column Exact",
          "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 \"Exact (D. Poilblanc, unpublished)\" 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#14 (qmbl-verify 2026-10-23); ruled 2026-10-24 (exact rows whose label reads as sampled)",
          "from": true
        }
      ],
      "sampled": false
    },
    {
      "energy": -15.95672,
      "sigma": 0.00026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "VMC",
      "ansatz": "RVB",
      "method_detail": "RVB (projected BCS + Jastrow, no antiferromagnetic field)",
      "method_as_published": "E_VMC^RVB",
      "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": "Lugas, Spanu, Becca & Sorella, Finite compressibility in the low-doping region of the two-dimensional t-J model, Phys. Rev. B 74, 165122 (2006), doi:10.1103/PhysRevB.74.165122, arXiv:cond-mat/0606659",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0606659 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": "-0.61372(1)",
        "note": "Table II, J/t = 0.3, column E_VMC^RVB (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0606659v1 (the only arXiv version; PDF md5 475a6ff1..., pypdf layout and plain modes, out/.../work/layout.txt); journal PDF Phys. Rev. B 74, 165122 (published 2006-10-31, received 2006-06-26) not reached: journals.aps.org returned HTTP 401 to node fetch on 2026-10-24 (subscription); Crossref metadata (title, authors, volume, article number) agree with the stored reference",
          "location": "p. 7, Table II (4 holes on 26 sites), row J/t = 0.3, column E^RVB_VMC/L",
          "reported_as": "-0.61372(1) per site, units of t",
          "conversion": "-0.61372 x 26 = -15.95672; sigma 1e-5 x 26 = 0.00026",
          "note": "Stored total and sigma reproduce the printed cell; t = 1 per-site units (Eq. 1 with -n n/4, no shift); 4 holes, N_up = N_dn = 11; periodic; cluster shape inferred (5,1), supported by the exact-recompute group's diagonalization reproducing the printed Lanczos column on that cluster; QMBL ED at this J: -16.7080260768; row lies above it. Not a duplicate: the other rows on the instance are Sorella, PRB 64, 024512 Table I (VMC, LS, FN, SR at 4 decimals, a 2001 computation with different printed numbers) and the quoted Poilblanc exact value. bound_type variational and sampled agree (VMC of Eq. 2). method_detail 'projected BCS + Jastrow': the text does not settle which Jastrow the RVB state carries (Table I caption: differs from Pfaff by Delta_AF only; Fig. 6 caption: Pfaff adds the spin Jastrow); left as is.",
          "source_entry": "tjP1-10-1103-physrevb-74-165122-c3#0 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -16.31552,
      "sigma": 0.00026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "FN-GFMC",
      "ansatz": "RVB",
      "method_detail": "lattice fixed node; projected BCS + Jastrow",
      "method_as_published": "E_FN^RVB",
      "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": "Lugas, Spanu, Becca & Sorella, Finite compressibility in the low-doping region of the two-dimensional t-J model, Phys. Rev. B 74, 165122 (2006), doi:10.1103/PhysRevB.74.165122, arXiv:cond-mat/0606659",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0606659 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": "-0.62752(1)",
        "note": "Table II, J/t = 0.3, column E_FN^RVB (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0606659v1 (the only arXiv version; PDF md5 475a6ff1..., pypdf layout and plain modes, out/.../work/layout.txt); journal PDF Phys. Rev. B 74, 165122 (published 2006-10-31, received 2006-06-26) not reached: journals.aps.org returned HTTP 401 to node fetch on 2026-10-24 (subscription); Crossref metadata (title, authors, volume, article number) agree with the stored reference",
          "location": "p. 7, Table II (4 holes on 26 sites), row J/t = 0.3, column E^RVB_FN/L",
          "reported_as": "-0.62752(1) per site, units of t",
          "conversion": "-0.62752 x 26 = -16.31552; sigma 1e-5 x 26 = 0.00026",
          "note": "Stored total and sigma reproduce the printed cell; t = 1 per-site units (Eq. 1 with -n n/4, no shift); 4 holes, N_up = N_dn = 11; periodic; cluster shape inferred (5,1), supported by the exact-recompute group's diagonalization reproducing the printed Lanczos column on that cluster; QMBL ED at this J: -16.7080260768; row lies above it. Not a duplicate: the other rows on the instance are Sorella, PRB 64, 024512 Table I (VMC, LS, FN, SR at 4 decimals, a 2001 computation with different printed numbers) and the quoted Poilblanc exact value. Lattice fixed node at gamma = 0 ('we will denote the standard FN energy for γ = 0 simply by E_FN', p. 5); the paper calls E^γ_FN 'a rigorous upper bound of the exact ground-state energy'; QMBL class projected per RULES 4 agrees.",
          "source_entry": "tjP1-10-1103-physrevb-74-165122-c3#1 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -15.98428,
      "sigma": 0.00026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "VMC",
      "ansatz": "Pfaffian",
      "method_detail": "projected BCS + antiferromagnetic field + Jastrow",
      "method_as_published": "E_VMC^Pfaff",
      "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": "Lugas, Spanu, Becca & Sorella, Finite compressibility in the low-doping region of the two-dimensional t-J model, Phys. Rev. B 74, 165122 (2006), doi:10.1103/PhysRevB.74.165122, arXiv:cond-mat/0606659",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0606659 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": "-0.61478(1)",
        "note": "Table II, J/t = 0.3, column E_VMC^Pfaff (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0606659v1 (the only arXiv version; PDF md5 475a6ff1..., pypdf layout and plain modes, out/.../work/layout.txt); journal PDF Phys. Rev. B 74, 165122 (published 2006-10-31, received 2006-06-26) not reached: journals.aps.org returned HTTP 401 to node fetch on 2026-10-24 (subscription); Crossref metadata (title, authors, volume, article number) agree with the stored reference",
          "location": "p. 7, Table II (4 holes on 26 sites), row J/t = 0.3, column E^Pfaff_VMC/L",
          "reported_as": "-0.61478(1) per site, units of t",
          "conversion": "-0.61478 x 26 = -15.98428; sigma 1e-5 x 26 = 0.00026",
          "note": "Stored total and sigma reproduce the printed cell; t = 1 per-site units (Eq. 1 with -n n/4, no shift); 4 holes, N_up = N_dn = 11; periodic; cluster shape inferred (5,1), supported by the exact-recompute group's diagonalization reproducing the printed Lanczos column on that cluster; QMBL ED at this J: -16.7080260768; row lies above it. Not a duplicate: the other rows on the instance are Sorella, PRB 64, 024512 Table I (VMC, LS, FN, SR at 4 decimals, a 2001 computation with different printed numbers) and the quoted Poilblanc exact value. bound_type variational and sampled agree (VMC of Eq. 2). The Pfaff state does not conserve S_z (AF field in the x-y plane, Eq. 6, projection onto fixed N only); still a bound on the N = 22 ground state.",
          "source_entry": "tjP1-10-1103-physrevb-74-165122-c3#2 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -16.31604,
      "sigma": 0.00026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "FN-GFMC",
      "ansatz": "Pfaffian",
      "method_detail": "lattice fixed node; projected BCS + antiferromagnetic field + Jastrow",
      "method_as_published": "E_FN^Pfaff",
      "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": "Lugas, Spanu, Becca & Sorella, Finite compressibility in the low-doping region of the two-dimensional t-J model, Phys. Rev. B 74, 165122 (2006), doi:10.1103/PhysRevB.74.165122, arXiv:cond-mat/0606659",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0606659 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": "-0.62754(1)",
        "note": "Table II, J/t = 0.3, column E_FN^Pfaff (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0606659v1 (the only arXiv version; PDF md5 475a6ff1..., pypdf layout and plain modes, out/.../work/layout.txt); journal PDF Phys. Rev. B 74, 165122 (published 2006-10-31, received 2006-06-26) not reached: journals.aps.org returned HTTP 401 to node fetch on 2026-10-24 (subscription); Crossref metadata (title, authors, volume, article number) agree with the stored reference",
          "location": "p. 7, Table II (4 holes on 26 sites), row J/t = 0.3, column E^Pfaff_FN/L",
          "reported_as": "-0.62754(1) per site, units of t",
          "conversion": "-0.62754 x 26 = -16.31604; sigma 1e-5 x 26 = 0.00026",
          "note": "Stored total and sigma reproduce the printed cell; t = 1 per-site units (Eq. 1 with -n n/4, no shift); 4 holes, N_up = N_dn = 11; periodic; cluster shape inferred (5,1), supported by the exact-recompute group's diagonalization reproducing the printed Lanczos column on that cluster; QMBL ED at this J: -16.7080260768; row lies above it. Not a duplicate: the other rows on the instance are Sorella, PRB 64, 024512 Table I (VMC, LS, FN, SR at 4 decimals, a 2001 computation with different printed numbers) and the quoted Poilblanc exact value. Lattice fixed node at gamma = 0 ('we will denote the standard FN energy for γ = 0 simply by E_FN', p. 5); the paper calls E^γ_FN 'a rigorous upper bound of the exact ground-state energy'; QMBL class projected per RULES 4 agrees.",
          "source_entry": "tjP1-10-1103-physrevb-74-165122-c3#3 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -16.36908,
      "sigma": 0.00078,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "FN-GFMC",
      "ansatz": "Pfaffian",
      "method_detail": "Eq. (15) finite-difference estimate, from fixed-node runs at γ = 0 and γ̃ = 1, of the expectation value of H over the γ = 0 fixed-node ground state (an upper bound to it)",
      "method_as_published": "Ẽ_Ψ0^γ=0 (Eq. 15, Pfaff)",
      "family": "AFQMC / GFMC",
      "bound_type": "projected",
      "bound_type_reason": "finite-difference estimate (Eq. 15) from fixed-node runs at γ = 0 and γ̃ = 1 of the expectation value of H over the γ = 0 fixed-node ground state, an upper bound within fixed node: 'Ẽ^{γ=0}_{Ψ0} certainly improves the standard FN upper bound of the energy and still Ẽ^{γ=0}_{Ψ0} ≥ E^{γ=0}_{Ψ0}' and 'we have computed Ẽ^{γ=0}_{Ψ0} using γ̃ = 1' (text after Fig. 9); not an extrapolation (ruled 2026-10-24)",
      "reference": "Lugas, Spanu, Becca & Sorella, Finite compressibility in the low-doping region of the two-dimensional t-J model, Phys. Rev. B 74, 165122 (2006), doi:10.1103/PhysRevB.74.165122, arXiv:cond-mat/0606659",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0606659 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": "-0.62958(3)",
        "note": "Table II, J/t = 0.3, column Ẽ_Ψ0^γ=0 (Eq. 15, Pfaff) (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).",
        "secondary_of": null
      }
    },
    {
      "energy": -15.9588,
      "sigma": 0.0026,
      "energy_variance": null,
      "dof": 22,
      "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, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0009149 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": "-0.6138(1)",
        "note": "Table I, N = 22, L = 26, J/t = 0.3, column VMC (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0009149v1 PDF, pypdf layout mode (table row parsed by out/tjP2-10-1103-physrevb-64-024512/build.py)",
          "location": "Table I (page 17), row N = 22, L = 26, J/t = 0.3, column VMC (layout text line 1050; header line 1049)",
          "reported_as": "-0.6138(1) per site, t = 1",
          "conversion": "-0.6138 x 26 = -15.9588; sigma 0.0001 x 26 = 0.0026",
          "note": "bound_type variational: 'VMC is the standard variational method'; Fig. 1 caption: 'the lowest energy Jastrow-Slater variational singlet wavefunction'. N = 22 electrons on L = 26 sites = 4 holes, N_up = N_dn = 11 (singlet); t = 1 and J/t from the row; energy per site, converted to total by x 26; sigma (1) in the last printed digit = 1e-4 per site (caption: 'statistical accuracy of 10^-4 t on the energy per site'). Hamiltonian not printed in this paper; the convention J(S.S - n n/4) and the sqrt(26) x sqrt(26) periodic cluster are fixed by the paper's ref. 23 (Poilblanc, PRB 52, 9201 (1995), arXiv:cond-mat/9505004v1, which prints H = t sum c+c + J sum (S.S - n n/4) on sqrt(N) x sqrt(N) clusters and footnote 17 '22 electrons on 26 sites'), by the exact column being reproduced on the (5, 1) cluster with that Hamiltonian (out/tjE-exact-recompute, this run), and by Lugas et al. PRB 74, 165122 Table II printing the same exact column. arXiv:cond-mat/0009149v1 (only arXiv version, 11 Sep 2000), PDF text by pypdf layout and plain mode (sources/tjP2-dl/cond-mat-0009149v1.layout.txt); journal version Phys. Rev. B 64, 024512 (2001) not reached: the APS PDF returned HTTP 401 from this session on 2026-10-24 (abstract page only: received 12 Sep 2000, published 19 Jun 2001).",
          "source_entry": "tjP2-10-1103-physrevb-64-024512#1 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -16.4632,
      "sigma": 0.0026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "VMC",
      "ansatz": "Gutzwiller",
      "method_detail": "projected BCS + Jastrow, 1 Lanczos step",
      "method_as_published": "VMC+LS",
      "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, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0009149 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": "-0.6332(1)",
        "note": "Table I, N = 22, L = 26, J/t = 0.3, column VMC+LS (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0009149v1 PDF, pypdf layout mode (table row parsed by out/tjP2-10-1103-physrevb-64-024512/build.py)",
          "location": "Table I (page 17), row N = 22, L = 26, J/t = 0.3, column VMC+LS (layout text line 1050; header line 1049)",
          "reported_as": "-0.6332(1) per site, t = 1",
          "conversion": "-0.6332 x 26 = -16.4632; sigma 0.0001 x 26 = 0.0026",
          "note": "bound_type variational: one Lanczos step on the variational state, sampled by the fixed-reference SR, which Sec. II.A calls 'rigorously variational'. N = 22 electrons on L = 26 sites = 4 holes, N_up = N_dn = 11 (singlet); t = 1 and J/t from the row; energy per site, converted to total by x 26; sigma (1) in the last printed digit = 1e-4 per site (caption: 'statistical accuracy of 10^-4 t on the energy per site'). Hamiltonian not printed in this paper; the convention J(S.S - n n/4) and the sqrt(26) x sqrt(26) periodic cluster are fixed by the paper's ref. 23 (Poilblanc, PRB 52, 9201 (1995), arXiv:cond-mat/9505004v1, which prints H = t sum c+c + J sum (S.S - n n/4) on sqrt(N) x sqrt(N) clusters and footnote 17 '22 electrons on 26 sites'), by the exact column being reproduced on the (5, 1) cluster with that Hamiltonian (out/tjE-exact-recompute, this run), and by Lugas et al. PRB 74, 165122 Table II printing the same exact column. arXiv:cond-mat/0009149v1 (only arXiv version, 11 Sep 2000), PDF text by pypdf layout and plain mode (sources/tjP2-dl/cond-mat-0009149v1.layout.txt); journal version Phys. Rev. B 64, 024512 (2001) not reached: the APS PDF returned HTTP 401 from this session on 2026-10-24 (abstract page only: received 12 Sep 2000, published 19 Jun 2001).",
          "source_entry": "tjP2-10-1103-physrevb-64-024512#2 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -16.3202,
      "sigma": 0.0026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "FN-GFMC",
      "ansatz": "Gutzwiller",
      "method_detail": "lattice fixed node; projected BCS + Jastrow",
      "method_as_published": "VMC+FN",
      "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, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0009149 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": "-0.6277(1)",
        "note": "Table I, N = 22, L = 26, J/t = 0.3, column VMC+FN (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0009149v1 PDF, pypdf layout mode (table row parsed by out/tjP2-10-1103-physrevb-64-024512/build.py)",
          "location": "Table I (page 17), row N = 22, L = 26, J/t = 0.3, column VMC+FN (layout text line 1050; header line 1049)",
          "reported_as": "-0.6277(1) per site, t = 1",
          "conversion": "-0.6277 x 26 = -16.3202; sigma 0.0001 x 26 = 0.0026",
          "note": "bound_type projected: 'VMC+FN is the lattice fixed node approach'; Sec. VI: 'the FN energy reported in the table is only an upper bound of the expectation value of the hamiltonian on the FN state'. N = 22 electrons on L = 26 sites = 4 holes, N_up = N_dn = 11 (singlet); t = 1 and J/t from the row; energy per site, converted to total by x 26; sigma (1) in the last printed digit = 1e-4 per site (caption: 'statistical accuracy of 10^-4 t on the energy per site'). Hamiltonian not printed in this paper; the convention J(S.S - n n/4) and the sqrt(26) x sqrt(26) periodic cluster are fixed by the paper's ref. 23 (Poilblanc, PRB 52, 9201 (1995), arXiv:cond-mat/9505004v1, which prints H = t sum c+c + J sum (S.S - n n/4) on sqrt(N) x sqrt(N) clusters and footnote 17 '22 electrons on 26 sites'), by the exact column being reproduced on the (5, 1) cluster with that Hamiltonian (out/tjE-exact-recompute, this run), and by Lugas et al. PRB 74, 165122 Table II printing the same exact column. arXiv:cond-mat/0009149v1 (only arXiv version, 11 Sep 2000), PDF text by pypdf layout and plain mode (sources/tjP2-dl/cond-mat-0009149v1.layout.txt); journal version Phys. Rev. B 64, 024512 (2001) not reached: the APS PDF returned HTTP 401 from this session on 2026-10-24 (abstract page only: received 12 Sep 2000, published 19 Jun 2001).",
          "source_entry": "tjP2-10-1103-physrevb-64-024512#3 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -16.5906,
      "sigma": 0.0026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "VMC",
      "ansatz": "Gutzwiller",
      "method_detail": "projected BCS + Jastrow, 2 Lanczos steps",
      "method_as_published": "VMC+2LS",
      "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, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0009149 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": "-0.6381(1)",
        "note": "Table I, N = 22, L = 26, J/t = 0.3, column VMC+2LS (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0009149v1 PDF, pypdf layout mode (table row parsed by out/tjP2-10-1103-physrevb-64-024512/build.py)",
          "location": "Table I (page 17), row N = 22, L = 26, J/t = 0.3, column VMC+2LS (layout text line 1050; header line 1049)",
          "reported_as": "-0.6381(1) per site, t = 1",
          "conversion": "-0.6381 x 26 = -16.5906; sigma 0.0001 x 26 = 0.0026",
          "note": "bound_type variational: two Lanczos steps on the variational state (Sec. II.A, 'rigorously variational'). N = 22 electrons on L = 26 sites = 4 holes, N_up = N_dn = 11 (singlet); t = 1 and J/t from the row; energy per site, converted to total by x 26; sigma (1) in the last printed digit = 1e-4 per site (caption: 'statistical accuracy of 10^-4 t on the energy per site'). Hamiltonian not printed in this paper; the convention J(S.S - n n/4) and the sqrt(26) x sqrt(26) periodic cluster are fixed by the paper's ref. 23 (Poilblanc, PRB 52, 9201 (1995), arXiv:cond-mat/9505004v1, which prints H = t sum c+c + J sum (S.S - n n/4) on sqrt(N) x sqrt(N) clusters and footnote 17 '22 electrons on 26 sites'), by the exact column being reproduced on the (5, 1) cluster with that Hamiltonian (out/tjE-exact-recompute, this run), and by Lugas et al. PRB 74, 165122 Table II printing the same exact column. arXiv:cond-mat/0009149v1 (only arXiv version, 11 Sep 2000), PDF text by pypdf layout and plain mode (sources/tjP2-dl/cond-mat-0009149v1.layout.txt); journal version Phys. Rev. B 64, 024512 (2001) not reached: the APS PDF returned HTTP 401 from this session on 2026-10-24 (abstract page only: received 12 Sep 2000, published 19 Jun 2001).",
          "source_entry": "tjP2-10-1103-physrevb-64-024512#4 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -16.5646,
      "sigma": 0.0026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "FN-GFMC",
      "ansatz": "Gutzwiller",
      "method_detail": "lattice fixed node; projected BCS + Jastrow, 1 Lanczos step",
      "method_as_published": "VMC+LS+FN",
      "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, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0009149 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": "-0.6371(1)",
        "note": "Table I, N = 22, L = 26, J/t = 0.3, column VMC+LS+FN (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0009149v1 PDF, pypdf layout mode (table row parsed by out/tjP2-10-1103-physrevb-64-024512/build.py)",
          "location": "Table I (page 17), row N = 22, L = 26, J/t = 0.3, column VMC+LS+FN (layout text line 1050; header line 1049)",
          "reported_as": "-0.6371(1) per site, t = 1",
          "conversion": "-0.6371 x 26 = -16.5646; sigma 0.0001 x 26 = 0.0026",
          "note": "bound_type projected: 'the fixed node over the VMC+LS wavefunction'. N = 22 electrons on L = 26 sites = 4 holes, N_up = N_dn = 11 (singlet); t = 1 and J/t from the row; energy per site, converted to total by x 26; sigma (1) in the last printed digit = 1e-4 per site (caption: 'statistical accuracy of 10^-4 t on the energy per site'). Hamiltonian not printed in this paper; the convention J(S.S - n n/4) and the sqrt(26) x sqrt(26) periodic cluster are fixed by the paper's ref. 23 (Poilblanc, PRB 52, 9201 (1995), arXiv:cond-mat/9505004v1, which prints H = t sum c+c + J sum (S.S - n n/4) on sqrt(N) x sqrt(N) clusters and footnote 17 '22 electrons on 26 sites'), by the exact column being reproduced on the (5, 1) cluster with that Hamiltonian (out/tjE-exact-recompute, this run), and by Lugas et al. PRB 74, 165122 Table II printing the same exact column. arXiv:cond-mat/0009149v1 (only arXiv version, 11 Sep 2000), PDF text by pypdf layout and plain mode (sources/tjP2-dl/cond-mat-0009149v1.layout.txt); journal version Phys. Rev. B 64, 024512 (2001) not reached: the APS PDF returned HTTP 401 from this session on 2026-10-24 (abstract page only: received 12 Sep 2000, published 19 Jun 2001).",
          "source_entry": "tjP2-10-1103-physrevb-64-024512#5 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -16.6062,
      "sigma": 0.0026,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "VMC",
      "ansatz": "Gutzwiller",
      "method_detail": "stochastic reconfiguration state at the best r, energy by forward walking",
      "method_as_published": "Best SR",
      "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, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0009149 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": "-0.6387(1)",
        "note": "Table I, N = 22, L = 26, J/t = 0.3, column Best SR (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0009149v1 PDF, pypdf layout mode (table row parsed by out/tjP2-10-1103-physrevb-64-024512/build.py)",
          "location": "Table I (page 17), row N = 22, L = 26, J/t = 0.3, column Best SR (layout text line 1050; header line 1049)",
          "reported_as": "-0.6387(1) per site, t = 1",
          "conversion": "-0.6387 x 26 = -16.6062; sigma 0.0001 x 26 = 0.0026",
          "note": "Record row (read hardest): energy, sigma, cluster, filling, couplings, column and provenance all agree; the number is the paper's own computation (no citation on the column). Lowest non-exact value on the instance; it sits above the exact value of the same table. bound_type variational: caption '\"Best r\" is <psiSR|H|psiSR>, computed by \"forward walking\" as described in App.(B), by optimizing the parameter r' (the caption's 'Best r' names the energy column Best SR; the Best r column holds r itself); Sec. III: '<psiSR|H|psiSR> >= E0 ... This estimate is obviously variational'. Best r printed for this row: 0.375. Not a mixed estimate: Fig. 2 shows the forward-walking convergence for 4 holes / 26 sites at J/t = 1. N = 22 electrons on L = 26 sites = 4 holes, N_up = N_dn = 11 (singlet); t = 1 and J/t from the row; energy per site, converted to total by x 26; sigma (1) in the last printed digit = 1e-4 per site (caption: 'statistical accuracy of 10^-4 t on the energy per site'). Hamiltonian not printed in this paper; the convention J(S.S - n n/4) and the sqrt(26) x sqrt(26) periodic cluster are fixed by the paper's ref. 23 (Poilblanc, PRB 52, 9201 (1995), arXiv:cond-mat/9505004v1, which prints H = t sum c+c + J sum (S.S - n n/4) on sqrt(N) x sqrt(N) clusters and footnote 17 '22 electrons on 26 sites'), by the exact column being reproduced on the (5, 1) cluster with that Hamiltonian (out/tjE-exact-recompute, this run), and by Lugas et al. PRB 74, 165122 Table II printing the same exact column. arXiv:cond-mat/0009149v1 (only arXiv version, 11 Sep 2000), PDF text by pypdf layout and plain mode (sources/tjP2-dl/cond-mat-0009149v1.layout.txt); journal version Phys. Rev. B 64, 024512 (2001) not reached: the APS PDF returned HTTP 401 from this session on 2026-10-24 (abstract page only: received 12 Sep 2000, published 19 Jun 2001).",
          "source_entry": "tjP2-10-1103-physrevb-64-024512#6 (qmbl-verify 2026-10-23)"
        }
      }
    }
  ],
  "url": "https://qmbl.org/i/tJ/square_26_P_h4_J0.3/",
  "per_site_divisor": 26,
  "per_site_label": "E/site",
  "best": {
    "exact": {
      "energy": -16.708026076752,
      "sigma": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "",
      "reference": "D. Poilblanc, unpublished exact diagonalization data on the 26-site t-J model, printed in Sorella, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), Table I, doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149 (acknowledgements)",
      "bound_type": "exact",
      "energy_per_site": -0.6426163875673846
    },
    "variational": {
      "energy": -16.6062,
      "sigma": 0.0026,
      "method": "VMC",
      "ansatz": "Gutzwiller",
      "method_detail": "stochastic reconfiguration state at the best r, energy by forward walking",
      "reference": "Sorella, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149",
      "bound_type": "variational",
      "energy_per_site": -0.6387
    },
    "projected": {
      "energy": -16.5646,
      "sigma": 0.0026,
      "method": "FN-GFMC",
      "ansatz": "Gutzwiller",
      "method_detail": "lattice fixed node; projected BCS + Jastrow, 1 Lanczos step",
      "reference": "Sorella, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149",
      "bound_type": "projected",
      "energy_per_site": -0.6371
    },
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -16.708026076752,
    "sigma": null,
    "method": "ED",
    "ansatz": null,
    "method_detail": "",
    "reference": "D. Poilblanc, unpublished exact diagonalization data on the 26-site t-J model, printed in Sorella, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001), Table I, doi:10.1103/PhysRevB.64.024512, arXiv:cond-mat/0009149 (acknowledgements)",
    "bound_type": "exact",
    "energy_per_site": -0.6426163875673846
  },
  "no_record_reason": null
}