{
  "model": "HEG3D",
  "lattice": "sc",
  "n_sites": 66,
  "boundary": "P",
  "params": {
    "N_up": 33,
    "N_dn": 33,
    "rs": 5,
    "twist": "Gamma"
  },
  "instance_id": "HEG3D/sc_66_P_33_33_5",
  "rows": [
    {
      "energy": -5.00478,
      "sigma": 0.00132,
      "energy_variance": null,
      "dof": 66,
      "einf": null,
      "v_score": null,
      "method": "Slater-Jastrow",
      "method_detail": "",
      "method_as_published": "VMC SJ",
      "family": "classic VMC",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Y. Kwon, D. M. Ceperley & R. M. Martin, Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study, Phys. Rev. B 58, 6800 (1998), arXiv:cond-mat/9803092, doi:10.1103/PhysRevB.58.6800",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-17",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-17",
        "method": "source text of arXiv:cond-mat/9803092 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": "-0.15166(4)",
        "note": "Table III, row N=66, rs=5.0; sources/cond-mat-9803092.txt line 657; printed in Ry per electron; version read: arXiv text (sources/cond-mat-9803092.txt), Tables II and III; APS copy not read | Ry per electron (converted × 1/2), N electrons in a cube with periodic boundary conditions (simple cubic). Checked against arXiv:0801.0518 on the same instance: the fixed-node DMC energy with backflow nodes, 1.0601(2) Ry = 0.53005 Ha at N = 54, rs = 1, agrees with its 0.52989(1) Ha, 0.0376 Ha below QMBL's HF energy 0.569245.",
        "secondary_of": null
      }
    },
    {
      "energy": -5.060616,
      "sigma": 0.000132,
      "energy_variance": null,
      "dof": 66,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "Slater-Jastrow (SJ) trial function, Jastrow factor not stated for this table (J1 Eq. 36 or J2 Eq. 39; conclusions, line 1543, say the pseudo",
      "method_as_published": "fixed-nodes DMC [Slater-Jastrow (SJ) trial function, Jastrow factor not stated for this table (J1 Eq. 36 or J2 Eq. 39; conclusions, line 1543, say the pseudo] (arXiv:1304.7298)",
      "family": "DMC",
      "bound_type": "projected",
      "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)",
      "reference": "Riccardo Fantoni, Radial distribution function in a diffusion Monte Carlo simulation of a Fermion fluid between the ideal gas and the Jellium model, Eur. Phys. J. B 86, 286, arXiv:1304.7298, doi:10.1140/epjb/e2013-40204-3",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:1304.7298 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": "-0.153352(4)",
        "note": "Table II, row rs = 5, column a; sources/1304.7298.txt line 982; printed in Ry per electron; version read: arXiv text in sources/; journal copy not read | Eq. (11) line 277: 'V = sum_{i<j} e^2 v_I(r_ij) + sum_i e^2 v_M', v_M = 1/2 lim_{r->0}[v_I(r) - v(r)] 'a Madelung constant ... interaction of a particle with its own images'; Ewald sums in Sec. III after Natoli and Ceperley (ref 34), background included (Eq. 8, 'uniform background of the same density but opposite charge'). Energies 'given in Rydbergs' (line 196-197). No Hartree-Fock energy is printed anywhere, so the convention cannot be fixed from the paper; the reader's check (see row notes) gives implied E-E_HF of -0.033 Ry (rs 10), -0.049 Ry (rs 5), -0.072 Ry (rs 2), -0.089 Ry (rs 1) per e",
        "secondary_of": null
      }
    },
    {
      "energy": -5.059857,
      "sigma": 0.000198,
      "energy_variance": null,
      "dof": 66,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "SJ trial function; time step tau = 0.1 (not ed); 4 walker numbers; 'optimal nw' 243",
      "method_as_published": "fixed-nodes DMC [SJ trial function; time step tau = 0.1 (not ed); 4 walker numbers; 'optimal nw' 243] (arXiv:1304.7298)",
      "family": "DMC",
      "bound_type": "projected",
      "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)",
      "reference": "Riccardo Fantoni, Radial distribution function in a diffusion Monte Carlo simulation of a Fermion fluid between the ideal gas and the Jellium model, Eur. Phys. J. B 86, 286, arXiv:1304.7298, doi:10.1140/epjb/e2013-40204-3",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:1304.7298 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": "-0.153329(6)",
        "note": "Table III, row rs = 5, column a; sources/1304.7298.txt line 999; printed in Ry per electron; version read: arXiv text in sources/; journal copy not read | Eq. (11) line 277: 'V = sum_{i<j} e^2 v_I(r_ij) + sum_i e^2 v_M', v_M = 1/2 lim_{r->0}[v_I(r) - v(r)] 'a Madelung constant ... interaction of a particle with its own images'; Ewald sums in Sec. III after Natoli and Ceperley (ref 34), background included (Eq. 8, 'uniform background of the same density but opposite charge'). Energies 'given in Rydbergs' (line 196-197). No Hartree-Fock energy is printed anywhere, so the convention cannot be fixed from the paper; the reader's check (see row notes) gives implied E-E_HF of -0.033 Ry (rs 10), -0.049 Ry (rs 5), -0.072 Ry (rs 2), -0.089 Ry (rs 1) per e",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG3D/sc_66_P_33_33_5/",
  "per_site_divisor": 66,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -5.060616,
    "sigma": 0.000132,
    "method": "Fixed-node DMC",
    "method_detail": "Slater-Jastrow (SJ) trial function, Jastrow factor not stated for this table (J1 Eq. 36 or J2 Eq. 39; conclusions, line 1543, say the pseudo",
    "reference": "Riccardo Fantoni, Radial distribution function in a diffusion Monte Carlo simulation of a Fermion fluid between the ideal gas and the Jellium model, Eur. Phys. J. B 86, 286, arXiv:1304.7298, doi:10.1140/epjb/e2013-40204-3",
    "bound_type": "projected",
    "energy_per_site": -0.076676
  },
  "no_record_reason": null
}