{
  "model": "HEG3D",
  "lattice": "sc",
  "n_sites": 19,
  "boundary": "P",
  "params": {
    "N_up": 19,
    "N_dn": 0,
    "rs": 50,
    "twist": "Gamma"
  },
  "instance_id": "HEG3D/sc_19_P_19_0_50",
  "rows": [
    {
      "energy": -0.276734525,
      "sigma": 4.75e-7,
      "energy_variance": null,
      "dof": 19,
      "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": "-0.02912995(5)",
        "note": "Table III column 2 (WAP-Net nd=1), block Ne = 19 (spin-polarised), row rs = 50.0; sources/2202.04622.txt line 534; 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": -0.27674849,
      "sigma": 3.8e-7,
      "energy_variance": null,
      "dof": 19,
      "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": "-0.02913142(4)",
        "note": "Table III column 3 (WAP-Net nd=8), block Ne = 19 (spin-polarised), row rs = 50.0; sources/2202.04622.txt line 534; 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": -0.276748965,
      "sigma": 4.75e-7,
      "energy_variance": null,
      "dof": 19,
      "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": "-0.02913147(5)",
        "note": "Table III column EIBVMC, block Ne = 19 (spin-polarised), row rs = 50.0; sources/2202.04622.txt line 534; 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": -0.276814705,
      "sigma": 7.6e-7,
      "energy_variance": null,
      "dof": 19,
      "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": "-0.02913839(8)",
        "note": "Table III column EIBDMC, block Ne = 19 (spin-polarised), row rs = 50.0; sources/2202.04622.txt line 534; 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": -0.27677015,
      "sigma": 5.7e-7,
      "energy_variance": null,
      "dof": 19,
      "einf": null,
      "v_score": null,
      "method": "MP-NQS",
      "method_detail": "plane-wave orbitals",
      "method_as_published": "MP-NQS (plane-wave orbitals)",
      "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": "G. Pescia, J. Nys, J. Kim, A. Lovato & G. Carleo, Message-passing neural quantum states for the homogeneous electron gas, Phys. Rev. B 110, 035108 (2024), arXiv:2305.07240, doi:10.1103/PhysRevB.110.035108",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-16",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-16",
        "method": "source text of arXiv:2305.07240 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": "−0.01456685(3)",
        "note": "Table IV (Appendix G), N=19 polarized, rs=50, column MP-NQS; sources/2305.07240.txt line 711; printed in Ha per electron; version read: arXiv text, Appendix G Tables I-V; APS copy not read | Ha per electron, simple cubic cell; Eq. 13 gives the Ewald sum and 'const.'. The WAP-net values it quotes equal arXiv:2202.04622's Table III (Madelung included) / 2 to 5e-7, and its own N = 14, rs = 1 energy sits 0.0376 Ha below QMBL's HF energy, as theirs does.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG3D/sc_19_P_19_0_50/",
  "per_site_divisor": 19,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -0.276814705,
    "sigma": 7.6e-7,
    "method": "Fixed-node DMC",
    "method_detail": "trial state: iterative backflow",
    "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": "projected",
    "energy_per_site": -0.014569195
  },
  "no_record_reason": null
}