{
  "model": "Hubbard",
  "lattice": "square",
  "n_sites": "inf",
  "boundary": "TDL",
  "params": {
    "U": 12,
    "n": 0.875
  },
  "instance_id": "Hubbard/square_inf_0.875_12",
  "rows": [
    {
      "energy": -0.6394,
      "sigma": 0.00001,
      "method": "DMET",
      "method_detail": "2 × 2",
      "method_as_published": "DMET, size 2 × 2, stripe wavelength d-wave",
      "bound_type": "approximate",
      "bound_type_reason": "series expansion, spin-wave theory or another fixed approximation; error of unknown sign (RULES.md 14.4)",
      "how_tdl": "series or approximate theory",
      "reference": "Zheng et al., Stripe order in the underdoped region of the two-dimensional Hubbard model, Science 358, 1155-1160 (2017), arXiv:1701.00054",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1701.00054: arXiv text and the journal's Supplementary Materials (pypdf layout and plain, read locally; version: 1701.00054v3 (main text); Supplementary Materials = Science SM file aan7127_Zheng_SM.pdf from CaltechAUTHORS record 73807 (the arXiv v3 PDF does not contain the SM; arXiv v1/v2 contain an older SM with Tables 1-7, different from Science Tables S1-S10)); journal version not read (publisher returned 403 to scripted access); single reading",
        "reported_as": "−0.63940 (error 0.00001); table columns 'Energy (t)' and 'Error (t)'",
        "note": "Table S4 (U/t = 12), row 'DMET 2 × 2'; line 212 of sources/zheng_science_SM.plain.txt (layout txt has the same digits) (sources/zheng_science_SM.plain.txt) | per site; units t; Main text Eq. (1) (sources/zheng.plain.txt, p. 2): H = -sum_{<ij>, sigma in {up,down}} t a^dag_{i sigma} a_{j sigma} + U sum_i n_{i up} n_{i down}; t, U are 'the kinetic and repulsion energies'; the Hermitian-conjugate term is not printed, bond counting not stated | The minus sign of the Science SM energies is extracted as a NUL byte (not as a minus character); it is present in the rendered PDF page (checked visually on pages 6-9: all energies are negative) and in the arXiv v2 SM text for rows that exist there. Value digits as in extracted text. Doping 1/8 is from main text (Fig. 6 caption); the SM table caption does not state the doping.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.6505,
      "sigma": 0.0001,
      "method": "DMET",
      "method_detail": "4 × 2 (SF)",
      "method_as_published": "DMET, size 4 × 2 (SF), stripe wavelength 4",
      "bound_type": "approximate",
      "bound_type_reason": "series expansion, spin-wave theory or another fixed approximation; error of unknown sign (RULES.md 14.4)",
      "how_tdl": "series or approximate theory",
      "reference": "Zheng et al., Stripe order in the underdoped region of the two-dimensional Hubbard model, Science 358, 1155-1160 (2017), arXiv:1701.00054",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1701.00054: arXiv text and the journal's Supplementary Materials (pypdf layout and plain, read locally; version: 1701.00054v3 (main text); Supplementary Materials = Science SM file aan7127_Zheng_SM.pdf from CaltechAUTHORS record 73807 (the arXiv v3 PDF does not contain the SM; arXiv v1/v2 contain an older SM with Tables 1-7, different from Science Tables S1-S10)); journal version not read (publisher returned 403 to scripted access); single reading",
        "reported_as": "−0.6505 (error 0.0001); table columns 'Energy (t)' and 'Error (t)'",
        "note": "Table S4 (U/t = 12), row 'DMET 4 × 2 (SF)'; line 213 of sources/zheng_science_SM.plain.txt (layout txt has the same digits) (sources/zheng_science_SM.plain.txt) | per site; units t; Main text Eq. (1) (sources/zheng.plain.txt, p. 2): H = -sum_{<ij>, sigma in {up,down}} t a^dag_{i sigma} a_{j sigma} + U sum_i n_{i up} n_{i down}; t, U are 'the kinetic and repulsion energies'; the Hermitian-conjugate term is not printed, bond counting not stated | The minus sign of the Science SM energies is extracted as a NUL byte (not as a minus character); it is present in the rendered PDF page (checked visually on pages 6-9: all energies are negative) and in the arXiv v2 SM text for rows that exist there. Value digits as in extracted text. Doping 1/8 is from main text (Fig. 6 caption); the SM table caption does not state the doping.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.6531,
      "sigma": 0.0001,
      "method": "DMET",
      "method_detail": "5 × 2",
      "method_as_published": "DMET, size 5 × 2, stripe wavelength 5",
      "bound_type": "approximate",
      "bound_type_reason": "series expansion, spin-wave theory or another fixed approximation; error of unknown sign (RULES.md 14.4)",
      "how_tdl": "series or approximate theory",
      "reference": "Zheng et al., Stripe order in the underdoped region of the two-dimensional Hubbard model, Science 358, 1155-1160 (2017), arXiv:1701.00054",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1701.00054: arXiv text and the journal's Supplementary Materials (pypdf layout and plain, read locally; version: 1701.00054v3 (main text); Supplementary Materials = Science SM file aan7127_Zheng_SM.pdf from CaltechAUTHORS record 73807 (the arXiv v3 PDF does not contain the SM; arXiv v1/v2 contain an older SM with Tables 1-7, different from Science Tables S1-S10)); journal version not read (publisher returned 403 to scripted access); single reading",
        "reported_as": "−0.6531 (error 0.0001); table columns 'Energy (t)' and 'Error (t)'",
        "note": "Table S4 (U/t = 12), row 'DMET 5 × 2'; line 214 of sources/zheng_science_SM.plain.txt (layout txt has the same digits) (sources/zheng_science_SM.plain.txt) | per site; units t; Main text Eq. (1) (sources/zheng.plain.txt, p. 2): H = -sum_{<ij>, sigma in {up,down}} t a^dag_{i sigma} a_{j sigma} + U sum_i n_{i up} n_{i down}; t, U are 'the kinetic and repulsion energies'; the Hermitian-conjugate term is not printed, bond counting not stated | The minus sign of the Science SM energies is extracted as a NUL byte (not as a minus character); it is present in the rendered PDF page (checked visually on pages 6-9: all energies are negative) and in the arXiv v2 SM text for rows that exist there. Value digits as in extracted text. Doping 1/8 is from main text (Fig. 6 caption); the SM table caption does not state the doping.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.6526,
      "sigma": 0.0002,
      "method": "DMET",
      "method_detail": "6 × 2 (SF)",
      "method_as_published": "DMET, size 6 × 2 (SF), stripe wavelength 6",
      "bound_type": "approximate",
      "bound_type_reason": "series expansion, spin-wave theory or another fixed approximation; error of unknown sign (RULES.md 14.4)",
      "how_tdl": "series or approximate theory",
      "reference": "Zheng et al., Stripe order in the underdoped region of the two-dimensional Hubbard model, Science 358, 1155-1160 (2017), arXiv:1701.00054",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1701.00054: arXiv text and the journal's Supplementary Materials (pypdf layout and plain, read locally; version: 1701.00054v3 (main text); Supplementary Materials = Science SM file aan7127_Zheng_SM.pdf from CaltechAUTHORS record 73807 (the arXiv v3 PDF does not contain the SM; arXiv v1/v2 contain an older SM with Tables 1-7, different from Science Tables S1-S10)); journal version not read (publisher returned 403 to scripted access); single reading",
        "reported_as": "−0.6526 (error 0.0002); table columns 'Energy (t)' and 'Error (t)'",
        "note": "Table S4 (U/t = 12), row 'DMET 6 × 2 (SF)'; line 215 of sources/zheng_science_SM.plain.txt (layout txt has the same digits) (sources/zheng_science_SM.plain.txt) | per site; units t; Main text Eq. (1) (sources/zheng.plain.txt, p. 2): H = -sum_{<ij>, sigma in {up,down}} t a^dag_{i sigma} a_{j sigma} + U sum_i n_{i up} n_{i down}; t, U are 'the kinetic and repulsion energies'; the Hermitian-conjugate term is not printed, bond counting not stated | The minus sign of the Science SM energies is extracted as a NUL byte (not as a minus character); it is present in the rendered PDF page (checked visually on pages 6-9: all energies are negative) and in the arXiv v2 SM text for rows that exist there. Value digits as in extracted text. Doping 1/8 is from main text (Fig. 6 caption); the SM table caption does not state the doping.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.6514,
      "sigma": 0.0001,
      "method": "DMET",
      "method_detail": "8 × 2 (SF)",
      "method_as_published": "DMET, size 8 × 2 (SF), stripe wavelength 8",
      "bound_type": "approximate",
      "bound_type_reason": "series expansion, spin-wave theory or another fixed approximation; error of unknown sign (RULES.md 14.4)",
      "how_tdl": "series or approximate theory",
      "reference": "Zheng et al., Stripe order in the underdoped region of the two-dimensional Hubbard model, Science 358, 1155-1160 (2017), arXiv:1701.00054",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1701.00054: arXiv text and the journal's Supplementary Materials (pypdf layout and plain, read locally; version: 1701.00054v3 (main text); Supplementary Materials = Science SM file aan7127_Zheng_SM.pdf from CaltechAUTHORS record 73807 (the arXiv v3 PDF does not contain the SM; arXiv v1/v2 contain an older SM with Tables 1-7, different from Science Tables S1-S10)); journal version not read (publisher returned 403 to scripted access); single reading",
        "reported_as": "−0.6514 (error 0.0001); table columns 'Energy (t)' and 'Error (t)'",
        "note": "Table S4 (U/t = 12), row 'DMET 8 × 2 (SF)'; line 216 of sources/zheng_science_SM.plain.txt (layout txt has the same digits) (sources/zheng_science_SM.plain.txt) | per site; units t; Main text Eq. (1) (sources/zheng.plain.txt, p. 2): H = -sum_{<ij>, sigma in {up,down}} t a^dag_{i sigma} a_{j sigma} + U sum_i n_{i up} n_{i down}; t, U are 'the kinetic and repulsion energies'; the Hermitian-conjugate term is not printed, bond counting not stated | The minus sign of the Science SM energies is extracted as a NUL byte (not as a minus character); it is present in the rendered PDF page (checked visually on pages 6-9: all energies are negative) and in the arXiv v2 SM text for rows that exist there. Value digits as in extracted text. Doping 1/8 is from main text (Fig. 6 caption); the SM table caption does not state the doping.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/instances/#x-Hubbard_square_inf_0_875_12",
  "per_site_divisor": 1,
  "per_site_label": "E/site",
  "best": {
    "exact": null,
    "variational": null,
    "projected": null,
    "extrapolated": null,
    "approximate": {
      "energy": -0.6531,
      "sigma": 0.0001,
      "method": "DMET",
      "ansatz": null,
      "method_detail": "5 × 2",
      "reference": "Zheng et al., Stripe order in the underdoped region of the two-dimensional Hubbard model, Science 358, 1155-1160 (2017), arXiv:1701.00054",
      "bound_type": "approximate",
      "energy_per_site": -0.6531
    },
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -0.6531,
    "sigma": 0.0001,
    "method": "DMET",
    "ansatz": null,
    "method_detail": "5 × 2",
    "reference": "Zheng et al., Stripe order in the underdoped region of the two-dimensional Hubbard model, Science 358, 1155-1160 (2017), arXiv:1701.00054",
    "bound_type": "approximate",
    "energy_per_site": -0.6531
  },
  "no_record_reason": null
}