{
  "model": "HEG3D",
  "lattice": "sc",
  "n_sites": 14,
  "boundary": "P",
  "params": {
    "N_up": 7,
    "N_dn": 7,
    "rs": 100,
    "twist": "Gamma"
  },
  "instance_id": "HEG3D/sc_14_P_7_7_100",
  "rows": [
    {
      "energy": -0.10822336,
      "sigma": 2.1e-7,
      "energy_variance": null,
      "dof": 14,
      "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": "-0.01546048(3)",
        "note": "Table III column 2 (WAP-Net nd=1), block Ne = 14 (paramagnetic), row rs = 100.0; sources/2202.04622.txt line 523; 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": -0.10821972,
      "sigma": 2.1e-7,
      "energy_variance": null,
      "dof": 14,
      "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": "-0.01545996(3)",
        "note": "Table III column 3 (WAP-Net nd=8), block Ne = 14 (paramagnetic), row rs = 100.0; sources/2202.04622.txt line 523; 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": -0.10818675,
      "sigma": 4.2e-7,
      "energy_variance": null,
      "dof": 14,
      "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": "-0.01545525(6)",
        "note": "Table III column EIBVMC, block Ne = 14 (paramagnetic), row rs = 100.0; sources/2202.04622.txt line 523; 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": -0.10828013,
      "sigma": 3.5e-7,
      "energy_variance": null,
      "dof": 14,
      "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": "-0.01546859(5)",
        "note": "Table III column EIBDMC, block Ne = 14 (paramagnetic), row rs = 100.0; sources/2202.04622.txt line 523; 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": -0.10822252,
      "sigma": 4.2e-7,
      "energy_variance": null,
      "dof": 14,
      "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": "−0.00773018(3)",
        "note": "Table I (Appendix G), N=14 unpolarized, rs=100, column MP-NQS; sources/2305.07240.txt line 668; 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
      }
    },
    {
      "energy": -0.0904437174354,
      "sigma": null,
      "energy_variance": null,
      "dof": 14,
      "einf": null,
      "v_score": null,
      "method": "CCD",
      "method_detail": "full CCD (driver, ladders, rings, crossed-rings, mosaics); equals CCSD in the HEG; extrapolated: 1/M → 0 (complete basis)",
      "method_as_published": "CCD [full CCD (driver, ladders, rings, crossed-rings, mosaics); equals CCSD in the HEG; extrapolated: 1/M → 0 (complete basis)] (arXiv:1310.6806)",
      "family": "FCIQMC / CC",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "James J. Shepherd, Thomas M. Henderson, and Gustavo E. Scuseria, Coupled Cluster Channels in the Homogeneous Electron Gas, J. Chem. Phys. 140, 124102, arXiv:1310.6806, doi:10.1063/1.4867783",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:1310.6806 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": "E_c = -0.020",
        "note": "Table III, rs=100.0, column CCD; sources/1310.6806.txt line 512; printed in Ha, total; printed correlation energy -0.020, E = E_HF + E_c with E_HF = -0.00503169410253 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Sec. II (txt line 64-81): HF eigenvalues with the zero-momentum integral given by 'vM, the Madelung constant ... defined uniquely for a cell geometry and box length, and here we calculate it to be vM L ~ 2.8372'. No Ewald-sum statement beyond that. The paper prints correlation energies only, which do not depend on the Madelung term, and no Hartree-Fock energy.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG3D/sc_14_P_7_7_100/",
  "per_site_divisor": 14,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -0.10828013,
    "sigma": 3.5e-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": -0.007734295
  },
  "no_record_reason": null
}