{
  "model": "tJ",
  "lattice": "rectangular-6x16",
  "n_sites": 96,
  "boundary": "PO",
  "params": {
    "t": 1,
    "J": 0.35,
    "N_up": 44,
    "N_dn": 44,
    "nn_term": true
  },
  "cluster": "16 x 6 cylinder, periodic along the 6-site direction, open along the 16-site direction (arXiv:cond-mat/0103096, lines 344-346 and Table I)",
  "instance_id": "tJ/rectangular-6x16_96_PO_h8_J0.35",
  "rows": [
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      "energy": -52.284,
      "sigma": null,
      "energy_variance": null,
      "dof": 88,
      "einf": null,
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      "method": "DMRG",
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      "method_detail": "symmetric: SU(2)",
      "method_as_published": "SU(2) DMRG, m = 500",
      "family": "tensor network",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "McCulloch, Bishop & Gulacsi, Density matrix renormalization group algorithm and the two-dimensional t-J model, Philos. Mag. B 81, 1603 (2001), doi:10.1080/13642810110051782, arXiv:cond-mat/0103096",
      "peer_reviewed": true,
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        "method": "source text of arXiv:cond-mat/0103096 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": "−52.284",
        "note": "Table I, 16 x 6, J = 0.35, 8 holes, cylindrical boundaries, SU(2) basis, m = 500 (line 784); version read: arXiv text (sources/cond-mat-0103096.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, J = 0.35; Table I prints the total energy E of the 16 x 6 system with 8 holes and cylindrical boundary conditions.",
        "secondary_of": null,
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          "location": "Table I, row 'SU(2) 500'",
          "reported_as": "−52.284 (total energy, units of t)",
          "conversion": "none: total energy in units of t; stored -52.284",
          "note": "Hamiltonian Eq. (1) H = -t sum (c+c + H.c.) + J(sum S_i.S_j - 1/4 n_i n_j), nn pairs once, t = 1, J = 0.35 (Table I caption): the instance form; 16 x 6, 8 holes (88 electrons, SU(2) basis targets the singlet, N_up = N_dn = 44); 'periodic boundary conditions in the y direction and open boundary conditions in the (generally longer) x direction' (p. 7): periodic along the 6-site side = rectangular-6x16 PO; Table I E is the total energy (-52.65/96 = -0.548 per site); own SU(2) DMRG (the U(1) m = 1000 row is quoted from White & Scalapino 1999 and is not in QMBL); bound_type variational is right: finite-m DMRG, the text calls DMRG 'a variational upper bound on the energy'; no sigma exists for a DMRG energy; journal version (Philos. Mag. B 81, 1603) not reached: tandfonline.com PDF returned 403 on 2026-10-24; arXiv v1 is the only arXiv version; no duplicate on the instance (the data file holds only these four rows)",
          "source_entry": "tjP6-tj#0 (qmbl-verify 2026-10-23)"
        }
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        "bond_dimension": 500,
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        "reported_as": "method string: \"SU(2) DMRG, m = 500\"",
        "source": "the row's published method string (scripts/method_names.mjs, 2026-09-17)",
        "scope": "row",
        "confidence": "high",
        "note": "Only the numbers the method string states; nothing else about this run's cost is recorded."
      }
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    {
      "energy": -52.463,
      "sigma": null,
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      "dof": 88,
      "einf": null,
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      "method": "DMRG",
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      "method_detail": "symmetric: SU(2)",
      "method_as_published": "SU(2) DMRG, m = 800",
      "family": "tensor network",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "McCulloch, Bishop & Gulacsi, Density matrix renormalization group algorithm and the two-dimensional t-J model, Philos. Mag. B 81, 1603 (2001), doi:10.1080/13642810110051782, arXiv:cond-mat/0103096",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
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        "method": "source text of arXiv:cond-mat/0103096 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": "−52.463",
        "note": "Table I, 16 x 6, J = 0.35, 8 holes, cylindrical boundaries, SU(2) basis, m = 800 (line 786); version read: arXiv text (sources/cond-mat-0103096.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, J = 0.35; Table I prints the total energy E of the 16 x 6 system with 8 holes and cylindrical boundary conditions.",
        "secondary_of": null,
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          "location": "Table I, row 'SU(2) 800'",
          "reported_as": "−52.463 (total energy, units of t)",
          "conversion": "none: total energy in units of t; stored -52.463",
          "note": "Hamiltonian Eq. (1) H = -t sum (c+c + H.c.) + J(sum S_i.S_j - 1/4 n_i n_j), nn pairs once, t = 1, J = 0.35 (Table I caption): the instance form; 16 x 6, 8 holes (88 electrons, SU(2) basis targets the singlet, N_up = N_dn = 44); 'periodic boundary conditions in the y direction and open boundary conditions in the (generally longer) x direction' (p. 7): periodic along the 6-site side = rectangular-6x16 PO; Table I E is the total energy (-52.65/96 = -0.548 per site); own SU(2) DMRG (the U(1) m = 1000 row is quoted from White & Scalapino 1999 and is not in QMBL); bound_type variational is right: finite-m DMRG, the text calls DMRG 'a variational upper bound on the energy'; no sigma exists for a DMRG energy; journal version (Philos. Mag. B 81, 1603) not reached: tandfonline.com PDF returned 403 on 2026-10-24; arXiv v1 is the only arXiv version; no duplicate on the instance (the data file holds only these four rows)",
          "source_entry": "tjP6-tj#1 (qmbl-verify 2026-10-23)"
        }
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        "n_devices": null,
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        "bond_dimension": 800,
        "iterations": null,
        "reported_as": "method string: \"SU(2) DMRG, m = 800\"",
        "source": "the row's published method string (scripts/method_names.mjs, 2026-09-17)",
        "scope": "row",
        "confidence": "high",
        "note": "Only the numbers the method string states; nothing else about this run's cost is recorded."
      }
    },
    {
      "energy": -52.52,
      "sigma": null,
      "energy_variance": null,
      "dof": 88,
      "einf": null,
      "v_score": null,
      "method": "DMRG",
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      "method_detail": "symmetric: SU(2)",
      "method_as_published": "SU(2) DMRG, m = 1200",
      "family": "tensor network",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "McCulloch, Bishop & Gulacsi, Density matrix renormalization group algorithm and the two-dimensional t-J model, Philos. Mag. B 81, 1603 (2001), doi:10.1080/13642810110051782, arXiv:cond-mat/0103096",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0103096 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": "−52.520",
        "note": "Table I, 16 x 6, J = 0.35, 8 holes, cylindrical boundaries, SU(2) basis, m = 1200 (line 788); version read: arXiv text (sources/cond-mat-0103096.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, J = 0.35; Table I prints the total energy E of the 16 x 6 system with 8 holes and cylindrical boundary conditions.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0103096v1 PDF (sources/cond-mat-0103096v1.pdf, byte-identical to the repo copy), pypdf layout mode, read 2026-10-24",
          "location": "Table I, row 'SU(2) 1200'",
          "reported_as": "−52.520 (total energy, units of t)",
          "conversion": "none: total energy in units of t; stored -52.52",
          "note": "Hamiltonian Eq. (1) H = -t sum (c+c + H.c.) + J(sum S_i.S_j - 1/4 n_i n_j), nn pairs once, t = 1, J = 0.35 (Table I caption): the instance form; 16 x 6, 8 holes (88 electrons, SU(2) basis targets the singlet, N_up = N_dn = 44); 'periodic boundary conditions in the y direction and open boundary conditions in the (generally longer) x direction' (p. 7): periodic along the 6-site side = rectangular-6x16 PO; Table I E is the total energy (-52.65/96 = -0.548 per site); own SU(2) DMRG (the U(1) m = 1000 row is quoted from White & Scalapino 1999 and is not in QMBL); bound_type variational is right: finite-m DMRG, the text calls DMRG 'a variational upper bound on the energy'; no sigma exists for a DMRG energy; journal version (Philos. Mag. B 81, 1603) not reached: tandfonline.com PDF returned 403 on 2026-10-24; arXiv v1 is the only arXiv version; no duplicate on the instance (the data file holds only these four rows)",
          "source_entry": "tjP6-tj#2 (qmbl-verify 2026-10-23)"
        }
      },
      "compute": {
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        "device": null,
        "n_devices": null,
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        "bond_dimension": 1200,
        "iterations": null,
        "reported_as": "method string: \"SU(2) DMRG, m = 1200\"",
        "source": "the row's published method string (scripts/method_names.mjs, 2026-09-17)",
        "scope": "row",
        "confidence": "high",
        "note": "Only the numbers the method string states; nothing else about this run's cost is recorded."
      }
    },
    {
      "energy": -52.65,
      "sigma": 0.05,
      "energy_variance": null,
      "dof": 88,
      "einf": null,
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      "method": "DMRG",
      "ansatz": null,
      "method_detail": "symmetric: SU(2); extrapolated: truncation error → 0",
      "method_as_published": "SU(2) DMRG, m → ∞ (zero truncation error)",
      "family": "tensor network",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "McCulloch, Bishop & Gulacsi, Density matrix renormalization group algorithm and the two-dimensional t-J model, Philos. Mag. B 81, 1603 (2001), doi:10.1080/13642810110051782, arXiv:cond-mat/0103096",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:cond-mat/0103096 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": "−52.65 ± 0.05",
        "note": "Table I, 16 x 6, J = 0.35, 8 holes, cylindrical boundaries, estimate extrapolated to zero truncation error (line 789); version read: arXiv text (sources/cond-mat-0103096.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, J = 0.35; Table I prints the total energy E of the 16 x 6 system with 8 holes and cylindrical boundary conditions.",
        "secondary_of": null,
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          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:cond-mat/0103096v1 PDF (sources/cond-mat-0103096v1.pdf, byte-identical to the repo copy), pypdf layout mode, read 2026-10-24",
          "location": "Table I, row '- ∞' (caption: 'an estimate of the true energy, extrapolated to zero truncation error')",
          "reported_as": "−52.65 ± 0.05 (total energy, units of t)",
          "conversion": "none: total energy in units of t; stored -52.65",
          "note": "Hamiltonian Eq. (1) H = -t sum (c+c + H.c.) + J(sum S_i.S_j - 1/4 n_i n_j), nn pairs once, t = 1, J = 0.35 (Table I caption): the instance form; 16 x 6, 8 holes (88 electrons, SU(2) basis targets the singlet, N_up = N_dn = 44); 'periodic boundary conditions in the y direction and open boundary conditions in the (generally longer) x direction' (p. 7): periodic along the 6-site side = rectangular-6x16 PO; Table I E is the total energy (-52.65/96 = -0.548 per site); own SU(2) DMRG (the U(1) m = 1000 row is quoted from White & Scalapino 1999 and is not in QMBL); bound_type extrapolated is right (zero-truncation-error extrapolation, not a bound); sigma 0.05 is the printed ± of the extrapolation; internal check: the text says the m = 1200 energy is 'around 0.25% higher than the estimated true ground state energy' ((-52.520 + 52.65)/52.65 = 0.247%); journal version (Philos. Mag. B 81, 1603) not reached: tandfonline.com PDF returned 403 on 2026-10-24; arXiv v1 is the only arXiv version; no duplicate on the instance (the data file holds only these four rows)",
          "source_entry": "tjP6-tj#3 (qmbl-verify 2026-10-23)"
        }
      }
    }
  ],
  "url": "https://qmbl.org/i/tJ/rectangular-6x16_96_PO_h8_J0.35/",
  "per_site_divisor": 96,
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      "bound_type": "variational",
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      "reference": "McCulloch, Bishop & Gulacsi, Density matrix renormalization group algorithm and the two-dimensional t-J model, Philos. Mag. B 81, 1603 (2001), doi:10.1080/13642810110051782, arXiv:cond-mat/0103096",
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}