{
  "model": "HEG3D",
  "lattice": "sc",
  "n_sites": 7,
  "boundary": "P",
  "params": {
    "N_up": 7,
    "N_dn": 0,
    "rs": 100,
    "twist": "Gamma"
  },
  "instance_id": "HEG3D/sc_7_P_7_0_100",
  "rows": [
    {
      "energy": -0.054225815,
      "sigma": 7e-8,
      "energy_variance": null,
      "dof": 7,
      "einf": null,
      "v_score": null,
      "method": "WAP-net",
      "method_detail": "n_d = 1",
      "method_as_published": "WAP-net (n_d = 1)",
      "family": "other NQS",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2202.04622 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": "-0.01549309(2)",
        "note": "Table III column 2 (WAP-Net nd=1), block Ne = 7 (spin-polarised), row rs = 100.0; sources/2202.04622.txt line 511; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.05422564,
      "sigma": 3.5e-8,
      "energy_variance": null,
      "dof": 7,
      "einf": null,
      "v_score": null,
      "method": "WAP-net",
      "method_detail": "n_d = 8",
      "method_as_published": "WAP-net (n_d = 8)",
      "family": "other NQS",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2202.04622 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": "-0.01549304(1)",
        "note": "Table III column 3 (WAP-Net nd=8), block Ne = 7 (spin-polarised), row rs = 100.0; sources/2202.04622.txt line 511; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.05416698,
      "sigma": 2.45e-7,
      "energy_variance": null,
      "dof": 7,
      "einf": null,
      "v_score": null,
      "method": "Iterative backflow",
      "method_detail": "single determinant",
      "method_as_published": "IB-VMC (iterative backflow, single determinant)",
      "family": "backflow / Pfaffian",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2202.04622 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": "-0.01547628(7)",
        "note": "Table III column EIBVMC, block Ne = 7 (spin-polarised), row rs = 100.0; sources/2202.04622.txt line 511; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.05422375,
      "sigma": 3.5e-7,
      "energy_variance": null,
      "dof": 7,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "trial state: iterative backflow",
      "method_as_published": "IB-DMC (fixed-node DMC on the iterative-backflow state)",
      "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": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2202.04622 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": "-0.0154925(1)",
        "note": "Table III column EIBDMC, block Ne = 7 (spin-polarised), row rs = 100.0; sources/2202.04622.txt line 511; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG3D/sc_7_P_7_0_100/",
  "per_site_divisor": 7,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -0.054225815,
    "sigma": 7e-8,
    "method": "WAP-net",
    "method_detail": "n_d = 1",
    "reference": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139",
    "bound_type": "variational",
    "energy_per_site": -0.007746545
  },
  "no_record_reason": null
}