{
  "model": "Hubbard",
  "lattice": "rectangular-8x48",
  "n_sites": 384,
  "boundary": "P",
  "params": {
    "Nf": 176,
    "U": 8
  },
  "instance_id": "Hubbard/rectangular-8x48_384_P_176_8",
  "rows": [
    {
      "energy": -261.9264,
      "sigma": 0.0768,
      "energy_variance": null,
      "dof": 352,
      "einf": 645.3333333333334,
      "v_score": null,
      "method": "CP-AFQMC",
      "method_detail": "trial state: half-filled stripe, λ = 6",
      "method_as_published": "CP-AFQMC (half-filled stripe, λ = 6, fully periodic, no pinning fields)",
      "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": "Xu, Shi, Vitali, Qin & Zhang, Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187, doi:10.1103/PhysRevResearch.4.013239",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-07",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-07",
        "method": "source text of arXiv:2112.02187 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": "-0.6821(2)",
        "note": "Table II, row 48 x 8, column λ = 6 (half-filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons.",
        "secondary_of": null
      },
      "corrections": [
        {
          "field": "reference",
          "to": "Xu, Shi, Vitali, Qin & Zhang, Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187, doi:10.1103/PhysRevResearch.4.013239",
          "reported_as": "title page of arXiv:2112.02187v3: 'Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram'; Crossref 10.1103/PhysRevResearch.4.013239: 'Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram' (Physical Review Research 4(1), 013239, published 2022-03-28)",
          "location": "arXiv:2112.02187v3 p. 1; Crossref works/10.1103/PhysRevResearch.4.013239",
          "version_read": "arXiv:2112.02187v3 PDF (md5 e6220eb6..., = qmbl/sources/2112.02187.pdf), pypdf plain + layout text extracted locally; TeX source arXiv e-print v3 (haoxu_draft.tex lines 664-690); Crossref record of 10.1103/PhysRevResearch.4.013239",
          "conversion": "none (text field)",
          "checked_on": "2026-10-07",
          "reason": "Wrong title: 'Stripe order from the perspective of the Hubbard model' is the title of E. W. Huang, C. B. Mendl, H.-C. Jiang, B. Moritz & T. P. Devereaux, npj Quantum Materials 3 (2018) (printed so as ref. [47] of arXiv:2202.11741v3), not of the cited PRR 4, 013239, whose authors, journal, volume, page and arXiv id the reference gets right. The record-attempts dossier (D-6x48.md) cites Xu et al. by authors, journal and arXiv id without a title; the wrong title enters at make_rows.mjs line 145. Same error on all six Xu et al. rows. Value check passed: Table II row 48 x 8, column λ = 6, '-0.6821(2)' per site; -0.6821 x 384 = -261.9264 (stored -261.9264); sigma 0.0002 x 384 = 0.0768 (stored 0.0768). Fully periodic 48 x 8, U = 8, δ = 1/12 (352 electrons), t' = 0, no pinning field; CP-AFQMC mixed estimate with a fixed stripe trial ('without invoking the self-consistency loop'), 'not variational', so projected is right. No duplicate on the instance.",
          "source_entry": "RP6-hubbard-j1j2#4",
          "from": "Xu, Shi, Vitali, Qin & Zhang, Stripe order from the perspective of the Hubbard model, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187"
        },
        {
          "field": "verified.note",
          "edit": [
            "48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.",
            "48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons."
          ],
          "reported_as": "Table II row '48 × 8 -0.6821(2) -0.6854(2) -0.6852(2)'; caption 'at U = 8 and δ = 1/12 ... Fully periodic supercells'",
          "location": "arXiv:2112.02187v3 Table II, p. 7",
          "version_read": "arXiv:2112.02187v3 PDF (md5 e6220eb6..., = qmbl/sources/2112.02187.pdf), pypdf plain + layout text extracted locally; TeX source arXiv e-print v3 (haoxu_draft.tex lines 664-690); Crossref record of 10.1103/PhysRevResearch.4.013239",
          "conversion": "δ = 1/12 on 384 sites: 384 x 11/12 = 352 electrons = 176 + 176 (instance Nf = 176)",
          "checked_on": "2026-10-07",
          "reason": "The shared convention_check of make_rows.mjs (XU, line 146) describes the 48 x 6 row only; on the three 48 x 8 rows the verification note names the wrong torus and electron count. Text only, no number changes.",
          "source_entry": "RP6-hubbard-j1j2#5",
          "from": "Table II, row 48 x 8, column λ = 6 (half-filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.",
          "to": "Table II, row 48 x 8, column λ = 6 (half-filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons."
        }
      ]
    },
    {
      "energy": -263.1936,
      "sigma": 0.0768,
      "energy_variance": null,
      "dof": 352,
      "einf": 645.3333333333334,
      "v_score": null,
      "method": "CP-AFQMC",
      "method_detail": "trial state: 2/3-filled stripe, λ = 8",
      "method_as_published": "CP-AFQMC (2/3-filled stripe, λ = 8, fully periodic, no pinning fields)",
      "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": "Xu, Shi, Vitali, Qin & Zhang, Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187, doi:10.1103/PhysRevResearch.4.013239",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-07",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-07",
        "method": "source text of arXiv:2112.02187 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": "-0.6854(2)",
        "note": "Table II, row 48 x 8, column λ = 8 (2/3-filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons.",
        "secondary_of": null
      },
      "corrections": [
        {
          "field": "reference",
          "to": "Xu, Shi, Vitali, Qin & Zhang, Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187, doi:10.1103/PhysRevResearch.4.013239",
          "reported_as": "title page of arXiv:2112.02187v3: 'Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram'; Crossref 10.1103/PhysRevResearch.4.013239: 'Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram' (Physical Review Research 4(1), 013239, published 2022-03-28)",
          "location": "arXiv:2112.02187v3 p. 1; Crossref works/10.1103/PhysRevResearch.4.013239",
          "version_read": "arXiv:2112.02187v3 PDF (md5 e6220eb6..., = qmbl/sources/2112.02187.pdf), pypdf plain + layout text extracted locally; TeX source arXiv e-print v3 (haoxu_draft.tex lines 664-690); Crossref record of 10.1103/PhysRevResearch.4.013239",
          "conversion": "none (text field)",
          "checked_on": "2026-10-07",
          "reason": "Wrong title: 'Stripe order from the perspective of the Hubbard model' is the title of E. W. Huang, C. B. Mendl, H.-C. Jiang, B. Moritz & T. P. Devereaux, npj Quantum Materials 3 (2018) (printed so as ref. [47] of arXiv:2202.11741v3), not of the cited PRR 4, 013239, whose authors, journal, volume, page and arXiv id the reference gets right. The record-attempts dossier (D-6x48.md) cites Xu et al. by authors, journal and arXiv id without a title; the wrong title enters at make_rows.mjs line 145. Same error on all six Xu et al. rows. Value check passed: Table II row 48 x 8, column λ = 8, '-0.6854(2)' per site; -0.6854 x 384 = -263.1936 (stored -263.1936); sigma 0.0002 x 384 = 0.0768 (stored 0.0768). Fully periodic 48 x 8, U = 8, δ = 1/12 (352 electrons), t' = 0, no pinning field; CP-AFQMC mixed estimate with a fixed stripe trial ('without invoking the self-consistency loop'), 'not variational', so projected is right. No duplicate on the instance.",
          "source_entry": "RP6-hubbard-j1j2#6",
          "from": "Xu, Shi, Vitali, Qin & Zhang, Stripe order from the perspective of the Hubbard model, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187"
        },
        {
          "field": "verified.note",
          "edit": [
            "48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.",
            "48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons."
          ],
          "reported_as": "Table II row '48 × 8 -0.6821(2) -0.6854(2) -0.6852(2)'; caption 'at U = 8 and δ = 1/12 ... Fully periodic supercells'",
          "location": "arXiv:2112.02187v3 Table II, p. 7",
          "version_read": "arXiv:2112.02187v3 PDF (md5 e6220eb6..., = qmbl/sources/2112.02187.pdf), pypdf plain + layout text extracted locally; TeX source arXiv e-print v3 (haoxu_draft.tex lines 664-690); Crossref record of 10.1103/PhysRevResearch.4.013239",
          "conversion": "δ = 1/12 on 384 sites: 384 x 11/12 = 352 electrons = 176 + 176 (instance Nf = 176)",
          "checked_on": "2026-10-07",
          "reason": "The shared convention_check of make_rows.mjs (XU, line 146) describes the 48 x 6 row only; on the three 48 x 8 rows the verification note names the wrong torus and electron count. Text only, no number changes.",
          "source_entry": "RP6-hubbard-j1j2#7",
          "from": "Table II, row 48 x 8, column λ = 8 (2/3-filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.",
          "to": "Table II, row 48 x 8, column λ = 8 (2/3-filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons."
        }
      ]
    },
    {
      "energy": -263.1168,
      "sigma": 0.0768,
      "energy_variance": null,
      "dof": 352,
      "einf": 645.3333333333334,
      "v_score": null,
      "method": "CP-AFQMC",
      "method_detail": "trial state: filled stripe, λ = 12",
      "method_as_published": "CP-AFQMC (filled stripe, λ = 12, fully periodic, no pinning fields)",
      "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": "Xu, Shi, Vitali, Qin & Zhang, Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187, doi:10.1103/PhysRevResearch.4.013239",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-07",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-07",
        "method": "source text of arXiv:2112.02187 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": "-0.6852(2)",
        "note": "Table II, row 48 x 8, column λ = 12 (filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons.",
        "secondary_of": null
      },
      "corrections": [
        {
          "field": "reference",
          "to": "Xu, Shi, Vitali, Qin & Zhang, Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187, doi:10.1103/PhysRevResearch.4.013239",
          "reported_as": "title page of arXiv:2112.02187v3: 'Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram'; Crossref 10.1103/PhysRevResearch.4.013239: 'Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram' (Physical Review Research 4(1), 013239, published 2022-03-28)",
          "location": "arXiv:2112.02187v3 p. 1; Crossref works/10.1103/PhysRevResearch.4.013239",
          "version_read": "arXiv:2112.02187v3 PDF (md5 e6220eb6..., = qmbl/sources/2112.02187.pdf), pypdf plain + layout text extracted locally; TeX source arXiv e-print v3 (haoxu_draft.tex lines 664-690); Crossref record of 10.1103/PhysRevResearch.4.013239",
          "conversion": "none (text field)",
          "checked_on": "2026-10-07",
          "reason": "Wrong title: 'Stripe order from the perspective of the Hubbard model' is the title of E. W. Huang, C. B. Mendl, H.-C. Jiang, B. Moritz & T. P. Devereaux, npj Quantum Materials 3 (2018) (printed so as ref. [47] of arXiv:2202.11741v3), not of the cited PRR 4, 013239, whose authors, journal, volume, page and arXiv id the reference gets right. The record-attempts dossier (D-6x48.md) cites Xu et al. by authors, journal and arXiv id without a title; the wrong title enters at make_rows.mjs line 145. Same error on all six Xu et al. rows. Value check passed: Table II row 48 x 8, column λ = 12, '-0.6852(2)' per site; -0.6852 x 384 = -263.1168 (stored -263.1168); sigma 0.0002 x 384 = 0.0768 (stored 0.0768). Fully periodic 48 x 8, U = 8, δ = 1/12 (352 electrons), t' = 0, no pinning field; CP-AFQMC mixed estimate with a fixed stripe trial ('without invoking the self-consistency loop'), 'not variational', so projected is right. No duplicate on the instance.",
          "source_entry": "RP6-hubbard-j1j2#8",
          "from": "Xu, Shi, Vitali, Qin & Zhang, Stripe order from the perspective of the Hubbard model, Phys. Rev. Research 4, 013239 (2022), arXiv:2112.02187"
        },
        {
          "field": "verified.note",
          "edit": [
            "48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.",
            "48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons."
          ],
          "reported_as": "Table II row '48 × 8 -0.6821(2) -0.6854(2) -0.6852(2)'; caption 'at U = 8 and δ = 1/12 ... Fully periodic supercells'",
          "location": "arXiv:2112.02187v3 Table II, p. 7",
          "version_read": "arXiv:2112.02187v3 PDF (md5 e6220eb6..., = qmbl/sources/2112.02187.pdf), pypdf plain + layout text extracted locally; TeX source arXiv e-print v3 (haoxu_draft.tex lines 664-690); Crossref record of 10.1103/PhysRevResearch.4.013239",
          "conversion": "δ = 1/12 on 384 sites: 384 x 11/12 = 352 electrons = 176 + 176 (instance Nf = 176)",
          "checked_on": "2026-10-07",
          "reason": "The shared convention_check of make_rows.mjs (XU, line 146) describes the 48 x 6 row only; on the three 48 x 8 rows the verification note names the wrong torus and electron count. Text only, no number changes.",
          "source_entry": "RP6-hubbard-j1j2#9",
          "from": "Table II, row 48 x 8, column λ = 12 (filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.",
          "to": "Table II, row 48 x 8, column λ = 12 (filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 8 is QMBL's 8 x 48 torus with 176 + 176 electrons."
        }
      ]
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/rectangular-8x48_384_P_176_8/",
  "per_site_divisor": 384,
  "per_site_label": "E/site",
  "record": null,
  "no_record_reason": "no variational row"
}