{
  "model": "Hubbard",
  "lattice": "square",
  "n_sites": "inf",
  "boundary": "TDL",
  "params": {
    "U": 8,
    "n": 0.5
  },
  "instance_id": "Hubbard/square_inf_0.5_8",
  "rows": [
    {
      "energy": -1.066,
      "sigma": 0.002,
      "method": "CP-AFQMC",
      "method_detail": "Table III",
      "method_as_published": "constrained-path AFQMC (CPMC), twist-averaged boundary conditions, single-determinant trial wave functions (free-electron at low and intermediate densities, Sec. V), fit of Eq. (15)",
      "bound_type": "extrapolated",
      "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)",
      "how_tdl": "finite-size extrapolation",
      "reference": "Qin et al., Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method, Phys. Rev. B 94, 085103 (2016), arXiv:1605.09421",
      "peer_reviewed": true,
      "source": "tdl-2026-10-25",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-25",
        "method": "arXiv:1605.09421: journal version: Phys. Rev. B 94, 085103 (2016), PDF from journals.aps.org over the ETH network (journal/qin-prb.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1605.09421v2 (the task listed 1605.08794, which is a different (math.PR) paper))); single reading, journal check, second reading 2026-10-25",
        "reported_as": "−1.066(2)",
        "note": "Table III (column n = 0.5, row e0, U = 8); line; line 881 of qin.plain.txt (sources/qin.plain.txt) | per site; units t; Eq. (1): H = K + V = -sum_{i,j,s} t_ij (c^dag_{i,s} c_{j,s} + H.c.) + U sum_i n_{i up} n_{i down}; only nearest-neighbour uniform hopping t_ij = t (t' = 0), t is the energy unit (Sec. II.A, lines after Eq. 1) | Table III caption: 'Ground state energy and kinetic energy per site ... for low to intermediate densities at U = 4 and U = 8'. Away from half filling the constrained-path approximation is not exact.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/instances/#x-Hubbard_square_inf_0_5_8",
  "per_site_divisor": 1,
  "per_site_label": "E/site",
  "best": {
    "exact": null,
    "variational": null,
    "projected": null,
    "extrapolated": {
      "energy": -1.066,
      "sigma": 0.002,
      "method": "CP-AFQMC",
      "ansatz": null,
      "method_detail": "Table III",
      "reference": "Qin et al., Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method, Phys. Rev. B 94, 085103 (2016), arXiv:1605.09421",
      "bound_type": "extrapolated",
      "energy_per_site": -1.066
    },
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -1.066,
    "sigma": 0.002,
    "method": "CP-AFQMC",
    "ansatz": null,
    "method_detail": "Table III",
    "reference": "Qin et al., Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method, Phys. Rev. B 94, 085103 (2016), arXiv:1605.09421",
    "bound_type": "extrapolated",
    "energy_per_site": -1.066
  },
  "no_record_reason": null
}