{
  "model": "Hubbard",
  "lattice": "rectangular-6x32",
  "n_sites": 192,
  "boundary": "P",
  "params": {
    "Nf": 84,
    "U": 8
  },
  "instance_id": "Hubbard/rectangular-6x32_192_P_84_8",
  "rows": [
    {
      "energy": -143.6736,
      "sigma": null,
      "energy_variance": null,
      "dof": 168,
      "einf": 294,
      "v_score": null,
      "method": "VMC",
      "method_detail": "stripe λ = 8 + Jastrow + backflow",
      "method_as_published": "VMC, stripe λ = 8 (Jastrow + backflow)",
      "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": "Marino, Becca & Tocchio, Stripes in the extended t-t' Hubbard model: A Variational Monte Carlo analysis, SciPost Phys. 12, 180 (2022), arXiv:2111.04623",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-07",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-07",
        "method": "source text of arXiv:2111.04623 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-0.7483",
        "note": "Table 1 (U/t = 8, t' = 0), row Lx = 32, column 'Energy striped state (λ = 8)'; no per-value error bar | Energy per site in units of t on Lx x 6 ladders with 'periodic boundary conditions along both the x and the y directions', hole doping 1/8 (n = 7/8). 'The error bar on the energy is always smaller than 10^-4' is one statement for the whole table, not a per-value sigma.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-07",
          "scope": "value",
          "method": "arXiv:2111.04623v4 PDF (md5 9a4166ea..., = qmbl/sources/2111.04623.pdf), pypdf plain + layout text extracted locally; TeX source arXiv e-print v4 (MBT_Stripes_last.tex lines 146, 257-274, 389-412)",
          "location": "Table 1 (U/t = 8, t' = 0), row Lx = 32, column 'Energy striped state (λ = 8)', p. 7 (TeX line 268)",
          "reported_as": "-0.7483 per site, units of t ('The error bar on the energy is always smaller than 10−4')",
          "conversion": "-0.7483 x 192 = -143.6736 (stored -143.6736); sigma null (one bound for the whole table, not a per-value sigma)",
          "note": "C1: Eq. (1) t-t'-U Hubbard, no constant shift; t' = 0 here, so VarBench's plain Hubbard. C3: 'ladders with L = Lx × 6 sites and periodic boundary conditions along both the x and the y directions' (Sec. 2) -> rectangular-6x32_192_P; the group's 6 x 48 VarBench decks run ibc=0 ('periodic-periodic'). C4: δ = 1/8, N = 168 = 84 + 84 (N↑ = N↓ not printed; singlet BCS term of Eq. (9) in both states, and the group's deck for 6 x 48 uses nelup=126, neldo=162); stripe wavelength λ = 8 imposed (Lx = 2kλ). C5: U/t = 8, t' = 0. Variational VMC energy (Jastrow + backflow), own number; no per-value sigma, so the row cannot hold a record, as stored. No duplicate: the instance carries only this paper's two rows (created by this pass). SciPost Phys. 12, 180 not read (scipost.org bot check); arXiv v4 is dated after publication (2022-06-01). peer_reviewed true.",
          "source_entry": "RP6-hubbard-j1j2#12"
        }
      }
    },
    {
      "energy": -142.7904,
      "sigma": null,
      "energy_variance": null,
      "dof": 168,
      "einf": 294,
      "v_score": null,
      "method": "VMC",
      "method_detail": "uniform + Jastrow + backflow",
      "method_as_published": "VMC, uniform state (Jastrow + backflow)",
      "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": "Marino, Becca & Tocchio, Stripes in the extended t-t' Hubbard model: A Variational Monte Carlo analysis, SciPost Phys. 12, 180 (2022), arXiv:2111.04623",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-07",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-07",
        "method": "source text of arXiv:2111.04623 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-0.7437",
        "note": "Table 1 (U/t = 8, t' = 0), row Lx = 32, column 'Energy uniform state'; no per-value error bar | Energy per site in units of t on Lx x 6 ladders with 'periodic boundary conditions along both the x and the y directions', hole doping 1/8 (n = 7/8). 'The error bar on the energy is always smaller than 10^-4' is one statement for the whole table, not a per-value sigma.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-07",
          "scope": "value",
          "method": "arXiv:2111.04623v4 PDF (md5 9a4166ea..., = qmbl/sources/2111.04623.pdf), pypdf plain + layout text extracted locally; TeX source arXiv e-print v4 (MBT_Stripes_last.tex lines 146, 257-274, 389-412)",
          "location": "Table 1 (U/t = 8, t' = 0), row Lx = 32, column 'Energy uniform state', p. 7 (TeX line 268)",
          "reported_as": "-0.7437 per site, units of t ('The error bar on the energy is always smaller than 10−4')",
          "conversion": "-0.7437 x 192 = -142.7904 (stored -142.7904); sigma null (one bound for the whole table, not a per-value sigma)",
          "note": "C1: Eq. (1) t-t'-U Hubbard, no constant shift; t' = 0 here, so VarBench's plain Hubbard. C3: 'ladders with L = Lx × 6 sites and periodic boundary conditions along both the x and the y directions' (Sec. 2) -> rectangular-6x32_192_P; the group's 6 x 48 VarBench decks run ibc=0 ('periodic-periodic'). C4: δ = 1/8, N = 168 = 84 + 84 (N↑ = N↓ not printed; singlet BCS term of Eq. (9) in both states, and the group's deck for 6 x 48 uses nelup=126, neldo=162); uniform state (Δc = Δs = 0, Néel ΔAF allowed). C5: U/t = 8, t' = 0. Variational VMC energy (Jastrow + backflow), own number; no per-value sigma, so the row cannot hold a record, as stored. No duplicate: the instance carries only this paper's two rows (created by this pass). SciPost Phys. 12, 180 not read (scipost.org bot check); arXiv v4 is dated after publication (2022-06-01). peer_reviewed true.",
          "source_entry": "RP6-hubbard-j1j2#13"
        }
      }
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/rectangular-6x32_192_P_84_8/",
  "per_site_divisor": 192,
  "per_site_label": "E/site",
  "record": null,
  "no_record_reason": "sampled rows carry no error bar"
}