{
  "model": "HEG3D",
  "lattice": "sc",
  "n_sites": 54,
  "boundary": "P",
  "params": {
    "N_up": 27,
    "N_dn": 27,
    "rs": 50,
    "twist": "Gamma"
  },
  "instance_id": "HEG3D/sc_54_P_27_27_50",
  "rows": [
    {
      "energy": -0.783081,
      "sigma": 0.0000054,
      "energy_variance": null,
      "dof": 54,
      "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": "−0.0145015(1)",
        "note": "Table II (Appendix G), N=54 unpolarized, rs=50, column MP-NQS; sources/2305.07240.txt line 683; 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": -0.7829946,
      "sigma": 0.0000054,
      "energy_variance": null,
      "dof": 54,
      "einf": null,
      "v_score": null,
      "method": "MP-NQS",
      "method_detail": "Gaussian orbitals on bcc sites",
      "method_as_published": "MP-NQS (Gaussian orbitals on bcc sites)",
      "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": "−0.0144999(1)",
        "note": "Table II (Appendix G), N=54 unpolarized, rs=50, column MP-NQS (Gauss); sources/2305.07240.txt line 683; 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": -0.74898,
      "sigma": 0.00108,
      "energy_variance": null,
      "dof": 54,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "trial state: Slater-Jastrow",
      "method_as_published": "FN-DMC (Slater-Jastrow trial 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": "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": "−0.01387(2)",
        "note": "Table II (Appendix G), N=54 unpolarized, rs=50, column FN-DMC; sources/2305.07240.txt line 683; 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": -0.66042,
      "sigma": null,
      "energy_variance": null,
      "dof": 54,
      "einf": null,
      "v_score": null,
      "method": "CCD",
      "method_detail": "extrapolated: 1/M → 0 (complete basis)",
      "method_as_published": "CCD, complete-basis limit",
      "family": "FCIQMC / CC",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-17",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-17",
        "method": "source text of arXiv:2103.03176 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": "-0.01223",
        "note": "Table II, row rs=50.0, column CCD; sources/2103.03176.txt line 395; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.68418,
      "sigma": null,
      "energy_variance": null,
      "dof": 54,
      "einf": null,
      "v_score": null,
      "method": "DCD",
      "method_detail": "extrapolated: 1/M → 0 (complete basis)",
      "method_as_published": "DCD, complete-basis limit",
      "family": "FCIQMC / CC",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-17",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-17",
        "method": "source text of arXiv:2103.03176 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": "-0.01267",
        "note": "Table II, row rs=50.0, column DCD; sources/2103.03176.txt line 395; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.68202,
      "sigma": null,
      "energy_variance": null,
      "dof": 54,
      "einf": null,
      "v_score": null,
      "method": "TC-CCD",
      "method_detail": "correlator cutoff k_c = 4 × 2π/L; extrapolated: 1/M → 0 (complete basis)",
      "method_as_published": "TC-CCD (k_c = 4), complete-basis limit",
      "family": "FCIQMC / CC",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-17",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-17",
        "method": "source text of arXiv:2103.03176 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": "-0.01263",
        "note": "Table II, row rs=50.0, column TC-CCD; sources/2103.03176.txt line 395; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.",
        "secondary_of": null
      }
    },
    {
      "energy": -0.69174,
      "sigma": null,
      "energy_variance": null,
      "dof": 54,
      "einf": null,
      "v_score": null,
      "method": "TC-DCD",
      "method_detail": "correlator cutoff k_c = 4 × 2π/L; extrapolated: 1/M → 0 (complete basis)",
      "method_as_published": "TC-DCD (k_c = 4), complete-basis limit",
      "family": "FCIQMC / CC",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-17",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-17",
        "method": "source text of arXiv:2103.03176 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": "-0.01281",
        "note": "Table II, row rs=50.0, column TC-DCD; sources/2103.03176.txt line 395; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG3D/sc_54_P_27_27_50/",
  "per_site_divisor": 54,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -0.783081,
    "sigma": 0.0000054,
    "method": "MP-NQS",
    "method_detail": "plane-wave orbitals",
    "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",
    "bound_type": "variational",
    "energy_per_site": -0.0145015
  },
  "no_record_reason": null
}