{
  "model": "tJ",
  "lattice": "square",
  "n_sites": 26,
  "boundary": "P",
  "params": {
    "t": 1,
    "J": 0.8,
    "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_J0.8",
  "rows": [
    {
      "energy": -25.83386,
      "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": "-0.99361(1)",
        "note": "Table II, J/t = 0.8, column E_VMC^RVB (line 397); 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; abs page lists [v1] only), PDF parsed with pypdf layout mode (sources/tjP1c4-dl/cond-mat-0606659v1.layout.txt, identical to the repo's sources/cond-mat-0606659.txt in Table II); journal version Phys. Rev. B 74, 165122 not reached: journals.aps.org/prb/pdf/10.1103/PhysRevB.74.165122 returned HTTP 401 to node fetch on 2026-10-24",
          "location": "Table II (4 holes on 26 sites), row J/t = 0.8, column E^RVB_VMC/L (layout line 397)",
          "reported_as": "-0.99361(1) per site (E/L, units of t)",
          "conversion": "-0.99361 x 26 = -25.83386; sigma (1) x 1e-5 x 26 = 0.00026",
          "note": "Value and error bar agree with the stored row. Eq. (1) H = -t sum (c+c + h.c.) + J sum (S_i.S_j - n_i n_j/4), t = 1, the stored convention (no shift). 4 holes on 26 sites = 22 electrons, N_up = N_dn = 11 (Sz = 0 contains the singlet ground state). J/t = 0.8, no t'. Cluster: Lugas et al. print only '26 sites' and periodic boundaries (their L = 2l^2 rule excludes 26). The Lanczos column at J/t = 0.3, 0.5, 1.0 equals, digit for digit, the 'Exact' column of Sorella, PRB 64, 024512, Table I (N = 22, L = 26), which credits D. Poilblanc's unpublished 26-site data and cites Poilblanc, PRB 52, 9201 (arXiv:cond-mat/9505004v1) for '4 holes in 26 sites'. That paper uses 'small sqrt(N) x sqrt(N) N-site clusters ... N=18, 20 and 26' with 'full use of space group and spin inversion symmetries' giving 50 717 244 basis states for 22 electrons on 26 sites (footnote 17); 26!/(4! 11! 11!) / (26 translations x 4 rotations x 2 spin inversion) = 50 702 925 plus non-free orbits, which fits the chiral (5, 1) x (-1, 5) torus (point group C4, order-208 group). The instance's (5, 1) cluster is therefore supported by the exact source the paper's own numbers coincide with; still not printed by Lugas et al. (needs_review stays until QMBL's own 26-site diagonalisation, requested). Final variational Monte Carlo estimate of Eq. (2) with (Pfaff) or without (RVB) the antiferromagnetic field; variational. Duplicate check: no other row on the instance carries this number.",
          "source_entry": "tjP1-10-1103-physrevb-74-165122-c4#5 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -26.12376,
      "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": "-1.00476(1)",
        "note": "Table II, J/t = 0.8, column E_FN^RVB (line 397); 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; abs page lists [v1] only), PDF parsed with pypdf layout mode (sources/tjP1c4-dl/cond-mat-0606659v1.layout.txt, identical to the repo's sources/cond-mat-0606659.txt in Table II); journal version Phys. Rev. B 74, 165122 not reached: journals.aps.org/prb/pdf/10.1103/PhysRevB.74.165122 returned HTTP 401 to node fetch on 2026-10-24",
          "location": "Table II (4 holes on 26 sites), row J/t = 0.8, column E^RVB_FN/L (layout line 397)",
          "reported_as": "-1.00476(1) per site (E/L, units of t)",
          "conversion": "-1.00476 x 26 = -26.12376; sigma (1) x 1e-5 x 26 = 0.00026",
          "note": "Value and error bar agree with the stored row. Eq. (1) H = -t sum (c+c + h.c.) + J sum (S_i.S_j - n_i n_j/4), t = 1, the stored convention (no shift). 4 holes on 26 sites = 22 electrons, N_up = N_dn = 11 (Sz = 0 contains the singlet ground state). J/t = 0.8, no t'. Cluster: Lugas et al. print only '26 sites' and periodic boundaries (their L = 2l^2 rule excludes 26). The Lanczos column at J/t = 0.3, 0.5, 1.0 equals, digit for digit, the 'Exact' column of Sorella, PRB 64, 024512, Table I (N = 22, L = 26), which credits D. Poilblanc's unpublished 26-site data and cites Poilblanc, PRB 52, 9201 (arXiv:cond-mat/9505004v1) for '4 holes in 26 sites'. That paper uses 'small sqrt(N) x sqrt(N) N-site clusters ... N=18, 20 and 26' with 'full use of space group and spin inversion symmetries' giving 50 717 244 basis states for 22 electrons on 26 sites (footnote 17); 26!/(4! 11! 11!) / (26 translations x 4 rotations x 2 spin inversion) = 50 702 925 plus non-free orbits, which fits the chiral (5, 1) x (-1, 5) torus (point group C4, order-208 group). The instance's (5, 1) cluster is therefore supported by the exact source the paper's own numbers coincide with; still not printed by Lugas et al. (needs_review stays until QMBL's own 26-site diagonalisation, requested). bound_type projected fits (lattice fixed node, ten Haaf et al.; the paper proves E^γ_FN is 'a rigorous upper bound of the exact ground-state energy', Eq. 12); the stored bound_type_reason 'not a strict variational bound' is generic text and understates this. Duplicate check: no other row on the instance carries this number.",
          "source_entry": "tjP1-10-1103-physrevb-74-165122-c4#6 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -25.92434,
      "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": "-0.99709(1)",
        "note": "Table II, J/t = 0.8, column E_VMC^Pfaff (line 397); 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; abs page lists [v1] only), PDF parsed with pypdf layout mode (sources/tjP1c4-dl/cond-mat-0606659v1.layout.txt, identical to the repo's sources/cond-mat-0606659.txt in Table II); journal version Phys. Rev. B 74, 165122 not reached: journals.aps.org/prb/pdf/10.1103/PhysRevB.74.165122 returned HTTP 401 to node fetch on 2026-10-24",
          "location": "Table II (4 holes on 26 sites), row J/t = 0.8, column E^Pfaff_VMC/L (layout line 397)",
          "reported_as": "-0.99709(1) per site (E/L, units of t)",
          "conversion": "-0.99709 x 26 = -25.92434; sigma (1) x 1e-5 x 26 = 0.00026",
          "note": "Value and error bar agree with the stored row. Eq. (1) H = -t sum (c+c + h.c.) + J sum (S_i.S_j - n_i n_j/4), t = 1, the stored convention (no shift). 4 holes on 26 sites = 22 electrons, N_up = N_dn = 11 (Sz = 0 contains the singlet ground state). J/t = 0.8, no t'. Cluster: Lugas et al. print only '26 sites' and periodic boundaries (their L = 2l^2 rule excludes 26). The Lanczos column at J/t = 0.3, 0.5, 1.0 equals, digit for digit, the 'Exact' column of Sorella, PRB 64, 024512, Table I (N = 22, L = 26), which credits D. Poilblanc's unpublished 26-site data and cites Poilblanc, PRB 52, 9201 (arXiv:cond-mat/9505004v1) for '4 holes in 26 sites'. That paper uses 'small sqrt(N) x sqrt(N) N-site clusters ... N=18, 20 and 26' with 'full use of space group and spin inversion symmetries' giving 50 717 244 basis states for 22 electrons on 26 sites (footnote 17); 26!/(4! 11! 11!) / (26 translations x 4 rotations x 2 spin inversion) = 50 702 925 plus non-free orbits, which fits the chiral (5, 1) x (-1, 5) torus (point group C4, order-208 group). The instance's (5, 1) cluster is therefore supported by the exact source the paper's own numbers coincide with; still not printed by Lugas et al. (needs_review stays until QMBL's own 26-site diagonalisation, requested). Final variational Monte Carlo estimate of Eq. (2) with (Pfaff) or without (RVB) the antiferromagnetic field; variational. Duplicate check: no other row on the instance carries this number.",
          "source_entry": "tjP1-10-1103-physrevb-74-165122-c4#7 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -26.17134,
      "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": "-1.00659(1)",
        "note": "Table II, J/t = 0.8, column E_FN^Pfaff (line 397); 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; abs page lists [v1] only), PDF parsed with pypdf layout mode (sources/tjP1c4-dl/cond-mat-0606659v1.layout.txt, identical to the repo's sources/cond-mat-0606659.txt in Table II); journal version Phys. Rev. B 74, 165122 not reached: journals.aps.org/prb/pdf/10.1103/PhysRevB.74.165122 returned HTTP 401 to node fetch on 2026-10-24",
          "location": "Table II (4 holes on 26 sites), row J/t = 0.8, column E^Pfaff_FN/L (layout line 397)",
          "reported_as": "-1.00659(1) per site (E/L, units of t)",
          "conversion": "-1.00659 x 26 = -26.17134; sigma (1) x 1e-5 x 26 = 0.00026",
          "note": "Value and error bar agree with the stored row. Eq. (1) H = -t sum (c+c + h.c.) + J sum (S_i.S_j - n_i n_j/4), t = 1, the stored convention (no shift). 4 holes on 26 sites = 22 electrons, N_up = N_dn = 11 (Sz = 0 contains the singlet ground state). J/t = 0.8, no t'. Cluster: Lugas et al. print only '26 sites' and periodic boundaries (their L = 2l^2 rule excludes 26). The Lanczos column at J/t = 0.3, 0.5, 1.0 equals, digit for digit, the 'Exact' column of Sorella, PRB 64, 024512, Table I (N = 22, L = 26), which credits D. Poilblanc's unpublished 26-site data and cites Poilblanc, PRB 52, 9201 (arXiv:cond-mat/9505004v1) for '4 holes in 26 sites'. That paper uses 'small sqrt(N) x sqrt(N) N-site clusters ... N=18, 20 and 26' with 'full use of space group and spin inversion symmetries' giving 50 717 244 basis states for 22 electrons on 26 sites (footnote 17); 26!/(4! 11! 11!) / (26 translations x 4 rotations x 2 spin inversion) = 50 702 925 plus non-free orbits, which fits the chiral (5, 1) x (-1, 5) torus (point group C4, order-208 group). The instance's (5, 1) cluster is therefore supported by the exact source the paper's own numbers coincide with; still not printed by Lugas et al. (needs_review stays until QMBL's own 26-site diagonalisation, requested). bound_type projected fits (lattice fixed node, ten Haaf et al.; the paper proves E^γ_FN is 'a rigorous upper bound of the exact ground-state energy', Eq. 12); the stored bound_type_reason 'not a strict variational bound' is generic text and understates this. Duplicate check: no other row on the instance carries this number.",
          "source_entry": "tjP1-10-1103-physrevb-74-165122-c4#8 (qmbl-verify 2026-10-23)"
        }
      }
    },
    {
      "energy": -26.20956,
      "sigma": 0.00052,
      "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": "-1.00806(2)",
        "note": "Table II, J/t = 0.8, column Ẽ_Ψ0^γ=0 (Eq. 15, Pfaff) (line 397); 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": -26.450585746393,
      "sigma": null,
      "energy_variance": null,
      "dof": 22,
      "einf": null,
      "v_score": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "Lanczos",
      "method_as_published": "E_ex (Lanczos)",
      "family": "other",
      "bound_type": "exact",
      "bound_type_reason": "numerically exact reference as stated by the source (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": "-1.01733",
        "note": "Table II, J/t = 0.8, column E_ex (Lanczos) (line 397); the paper names no source for its Lanczos column, and its acknowledgements name only funding; the 4-hole values at J/t = 0.3, 0.5 and 1 equal digit for digit the Exact column of Sorella, Phys. Rev. B 64, 024512, Table I, whose acknowledgements credit D. Poilblanc's unpublished 26-site data (arXiv:cond-mat/0009149, lines 829-831); the row stays primary to this paper (ruled 2026-10-24); 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": "2026-10-23",
          "scope": "value",
          "method": "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 II, J/t = 0.8, column E_ex (Lanczos) (line 397)",
          "reported_as": "-1.01733",
          "conversion": "E = -26.4505857464 (t = 1); printed form E/L: -1.01733 vs printed -1.01733",
          "note": "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 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 sq26P_h4_J0.8_k0-0_l0_star1, dim 101410008; 9884 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": "tjE-exact-recompute#18 (qmbl-verify 2026-10-23)"
        }
      },
      "corrections": [
        {
          "field": "energy",
          "to": -26.450585746393,
          "reported_as": "-1.01733 (E/L)",
          "location": "Table II, J/t = 0.8, column E_ex (Lanczos) (line 397)",
          "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": "-1.01733 x 26 = -26.45058 (stored); recomputed -26.450585746393 = -1.0173302210 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 of 14 symmetry sectors, lowest sector sq26P_h4_J0.8_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#18 (qmbl-verify 2026-10-23); rule for recomputed exact rows, ruled 2026-10-24",
          "from": -26.45058
        },
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-1.01733",
          "location": "Table II, J/t = 0.8, column E_ex (Lanczos) (line 397)",
          "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 \"E_ex (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#18 (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/square_26_P_h4_J0.8/",
  "per_site_divisor": 26,
  "per_site_label": "E/site",
  "best": {
    "exact": {
      "energy": -26.450585746393,
      "sigma": null,
      "method": "ED",
      "ansatz": null,
      "method_detail": "Lanczos",
      "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",
      "bound_type": "exact",
      "energy_per_site": -1.0173302210151154
    },
    "variational": {
      "energy": -25.92434,
      "sigma": 0.00026,
      "method": "VMC",
      "ansatz": "Pfaffian",
      "method_detail": "projected BCS + antiferromagnetic field + Jastrow",
      "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",
      "bound_type": "variational",
      "energy_per_site": -0.99709
    },
    "projected": {
      "energy": -26.20956,
      "sigma": 0.00052,
      "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)",
      "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",
      "bound_type": "projected",
      "energy_per_site": -1.00806
    },
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -26.450585746393,
    "sigma": null,
    "method": "ED",
    "ansatz": null,
    "method_detail": "Lanczos",
    "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",
    "bound_type": "exact",
    "energy_per_site": -1.0173302210151154
  },
  "no_record_reason": null
}