{
  "model": "HEG3D",
  "lattice": "sc",
  "n_sites": 114,
  "boundary": "P",
  "params": {
    "N_up": 57,
    "N_dn": 57,
    "rs": 1,
    "twist": "Gamma"
  },
  "instance_id": "HEG3D/sc_114_P_57_57_1",
  "rows": [
    {
      "energy": 68.8503,
      "sigma": 0.0285,
      "energy_variance": null,
      "dof": 114,
      "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": "1.2079(5)",
        "note": "Table III, row N=114, rs=1.0; sources/cond-mat-9803092.txt line 658; 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": 68.25978,
      "sigma": 0.00684,
      "energy_variance": null,
      "dof": 114,
      "einf": null,
      "v_score": null,
      "method": "ph-AFQMC",
      "method_detail": "RHF trial, time step 0.005 a.u., 2880 walkers; basis M=2109",
      "method_as_published": "RHF+ph-AFQMC [RHF trial, time step 0.005 a.u., 2880 walkers; basis M=2109] (arXiv:1905.04361)",
      "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": "Joonho Lee, Fionn D. Malone, Miguel A. Morales, An Auxiliary-Field Quantum Monte Carlo Perspective on the Ground State of the Dense Uniform Electron Gas: An Investigation with Hartree-Fock Trial Wavefunctions, J. Chem. Phys. 151, 064122, arXiv:1905.04361, doi:10.1063/1.5109572",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:1905.04361 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": "0.59877(6)",
        "note": "Table VI, rs=1.0; sources/1905.04361.txt line 676; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Eq. (19) (txt line 210): H = T + Vee + E_M; txt lines 232-237: 'the Madelung energy E_M is included to account for the self-interaction of the Ewald sum under periodic boundary conditions. For simplicity we use the formula proposed by Schoof and co-workers' E_M ~ -2.837297 (3/4pi)^(1/3) N^(2/3)/rs (Eq. 22, txt line 238-239). So the Madelung term is included, but through the approximate closed form (Ref 76: T. Schoof, S. Groth, J. Vorberger, M. Bonitz, PRL 115, 130402 (2015)), not through a stated Ewald sum. No Hartree-Fock energy is printed. Reader's own check (python, scratch-R8/hf.py, NOT QM",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG3D/sc_114_P_57_57_1/",
  "per_site_divisor": 114,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": 68.25978,
    "sigma": 0.00684,
    "method": "ph-AFQMC",
    "method_detail": "RHF trial, time step 0.005 a.u., 2880 walkers; basis M=2109",
    "reference": "Joonho Lee, Fionn D. Malone, Miguel A. Morales, An Auxiliary-Field Quantum Monte Carlo Perspective on the Ground State of the Dense Uniform Electron Gas: An Investigation with Hartree-Fock Trial Wavefunctions, J. Chem. Phys. 151, 064122, arXiv:1905.04361, doi:10.1063/1.5109572",
    "bound_type": "projected",
    "energy_per_site": 0.59877
  },
  "no_record_reason": null
}