{
  "model": "HEG2D",
  "lattice": "square",
  "n_sites": 90,
  "boundary": "P",
  "params": {
    "N_up": 45,
    "N_dn": 45,
    "rs": 30,
    "twist": "Gamma"
  },
  "instance_id": "HEG2D/square_90_P_45_45_30",
  "rows": [
    {
      "energy": -2.856357,
      "sigma": 0.000018,
      "energy_variance": null,
      "dof": 90,
      "einf": null,
      "v_score": null,
      "method": "Slater-Jastrow",
      "method_detail": "Jastrow optimised at Gamma from random starting point 1",
      "method_as_published": "SJ-VMC [Jastrow optimised at Gamma from random starting point 1] (arXiv:2405.00425)",
      "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": "Sam Azadi, N. D. Drummond, and Sam M. Vinko, Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid, Phys. Rev. B 110, 245145, arXiv:2405.00425, doi:10.1103/PhysRevB.110.245145",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:2405.00425 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": "−0.0317373(2)",
        "note": "Table III, Γ start 1, column SJ-VMC; sources/2405.00425.txt line 371; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Table III (txt lines 371-376): the HF energy for the 90-electron square cell at rs=30 and Gamma is printed as -0.0196518 Ha/el. QMBL's own checks/heg-hf/hf.mjs (2 square 45 45 30, Gamma) gives -0.0196517776 (Ewald sum, uniform background, Madelung term included), so Hartree units, per electron and Ewald with Madelung included are fixed by that number. No sentence in the text names the Ewald sum or the Madelung term. Fig. 4 caption (txt line 505) subtracts 'the Madelung energy of a hexagonal lattice, -vM0/rs' from DMC energies, consistent with energies that contain the Madelung term. The Balder",
        "secondary_of": null
      }
    },
    {
      "energy": -2.262582,
      "sigma": 0.000072,
      "energy_variance": null,
      "dof": 90,
      "einf": null,
      "v_score": null,
      "method": "Slater-Jastrow",
      "method_detail": "Jastrow optimised at Gamma from random starting point 2",
      "method_as_published": "SJ-VMC [Jastrow optimised at Gamma from random starting point 2] (arXiv:2405.00425)",
      "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": "Sam Azadi, N. D. Drummond, and Sam M. Vinko, Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid, Phys. Rev. B 110, 245145, arXiv:2405.00425, doi:10.1103/PhysRevB.110.245145",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:2405.00425 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": "−0.0251398(8)",
        "note": "Table III, Γ start 2, column SJ-VMC; sources/2405.00425.txt line 372; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Table III (txt lines 371-376): the HF energy for the 90-electron square cell at rs=30 and Gamma is printed as -0.0196518 Ha/el. QMBL's own checks/heg-hf/hf.mjs (2 square 45 45 30, Gamma) gives -0.0196517776 (Ewald sum, uniform background, Madelung term included), so Hartree units, per electron and Ewald with Madelung included are fixed by that number. No sentence in the text names the Ewald sum or the Madelung term. Fig. 4 caption (txt line 505) subtracts 'the Madelung energy of a hexagonal lattice, -vM0/rs' from DMC energies, consistent with energies that contain the Madelung term. The Balder",
        "secondary_of": null
      }
    },
    {
      "energy": -2.443554,
      "sigma": 0.000063,
      "energy_variance": null,
      "dof": 90,
      "einf": null,
      "v_score": null,
      "method": "Slater-Jastrow",
      "method_detail": "Jastrow optimised at Gamma from random starting point 3",
      "method_as_published": "SJ-VMC [Jastrow optimised at Gamma from random starting point 3] (arXiv:2405.00425)",
      "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": "Sam Azadi, N. D. Drummond, and Sam M. Vinko, Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid, Phys. Rev. B 110, 245145, arXiv:2405.00425, doi:10.1103/PhysRevB.110.245145",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:2405.00425 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": "−0.0271506(7)",
        "note": "Table III, Γ start 3, column SJ-VMC; sources/2405.00425.txt line 373; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Table III (txt lines 371-376): the HF energy for the 90-electron square cell at rs=30 and Gamma is printed as -0.0196518 Ha/el. QMBL's own checks/heg-hf/hf.mjs (2 square 45 45 30, Gamma) gives -0.0196517776 (Ewald sum, uniform background, Madelung term included), so Hartree units, per electron and Ewald with Madelung included are fixed by that number. No sentence in the text names the Ewald sum or the Madelung term. Fig. 4 caption (txt line 505) subtracts 'the Madelung energy of a hexagonal lattice, -vM0/rs' from DMC energies, consistent with energies that contain the Madelung term. The Balder",
        "secondary_of": null
      }
    },
    {
      "energy": -2.8359,
      "sigma": 0.0018,
      "energy_variance": null,
      "dof": 90,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "HF nodes; twist Gamma",
      "method_as_published": "S-DMC (Slater-only fixed-node DMC) [HF nodes; twist Gamma] (arXiv:2405.00425)",
      "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": "Sam Azadi, N. D. Drummond, and Sam M. Vinko, Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid, Phys. Rev. B 110, 245145, arXiv:2405.00425, doi:10.1103/PhysRevB.110.245145",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:2405.00425 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": "−0.03151(2)",
        "note": "Table IV, Γ start 1, column S-DMC; sources/2405.00425.txt line 387; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Table III (txt lines 371-376): the HF energy for the 90-electron square cell at rs=30 and Gamma is printed as -0.0196518 Ha/el. QMBL's own checks/heg-hf/hf.mjs (2 square 45 45 30, Gamma) gives -0.0196517776 (Ewald sum, uniform background, Madelung term included), so Hartree units, per electron and Ewald with Madelung included are fixed by that number. No sentence in the text names the Ewald sum or the Madelung term. Fig. 4 caption (txt line 505) subtracts 'the Madelung energy of a hexagonal lattice, -vM0/rs' from DMC energies, consistent with energies that contain the Madelung term. The Balder",
        "secondary_of": null
      }
    },
    {
      "energy": -2.87271,
      "sigma": 0.00009,
      "energy_variance": null,
      "dof": 90,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "Jastrow optimised at Gamma, start 1",
      "method_as_published": "SJ-DMC [Jastrow optimised at Gamma, start 1] (arXiv:2405.00425)",
      "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": "Sam Azadi, N. D. Drummond, and Sam M. Vinko, Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid, Phys. Rev. B 110, 245145, arXiv:2405.00425, doi:10.1103/PhysRevB.110.245145",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:2405.00425 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": "−0.031919(1)",
        "note": "Table IV, Γ start 1, column SJ-DMC; sources/2405.00425.txt line 387; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Table III (txt lines 371-376): the HF energy for the 90-electron square cell at rs=30 and Gamma is printed as -0.0196518 Ha/el. QMBL's own checks/heg-hf/hf.mjs (2 square 45 45 30, Gamma) gives -0.0196517776 (Ewald sum, uniform background, Madelung term included), so Hartree units, per electron and Ewald with Madelung included are fixed by that number. No sentence in the text names the Ewald sum or the Madelung term. Fig. 4 caption (txt line 505) subtracts 'the Madelung energy of a hexagonal lattice, -vM0/rs' from DMC energies, consistent with energies that contain the Madelung term. The Balder",
        "secondary_of": null
      }
    },
    {
      "energy": -2.4084,
      "sigma": 0.0063,
      "energy_variance": null,
      "dof": 90,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "Jastrow optimised at Gamma, start 2",
      "method_as_published": "SJ-DMC [Jastrow optimised at Gamma, start 2] (arXiv:2405.00425)",
      "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": "Sam Azadi, N. D. Drummond, and Sam M. Vinko, Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid, Phys. Rev. B 110, 245145, arXiv:2405.00425, doi:10.1103/PhysRevB.110.245145",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:2405.00425 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": "−0.02676(7)",
        "note": "Table IV, Γ start 2, column SJ-DMC; sources/2405.00425.txt line 388; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Table III (txt lines 371-376): the HF energy for the 90-electron square cell at rs=30 and Gamma is printed as -0.0196518 Ha/el. QMBL's own checks/heg-hf/hf.mjs (2 square 45 45 30, Gamma) gives -0.0196517776 (Ewald sum, uniform background, Madelung term included), so Hartree units, per electron and Ewald with Madelung included are fixed by that number. No sentence in the text names the Ewald sum or the Madelung term. Fig. 4 caption (txt line 505) subtracts 'the Madelung energy of a hexagonal lattice, -vM0/rs' from DMC energies, consistent with energies that contain the Madelung term. The Balder",
        "secondary_of": null
      }
    },
    {
      "energy": -2.5632,
      "sigma": 0.0018,
      "energy_variance": null,
      "dof": 90,
      "einf": null,
      "v_score": null,
      "method": "Fixed-node DMC",
      "method_detail": "Jastrow optimised at Gamma, start 3",
      "method_as_published": "SJ-DMC [Jastrow optimised at Gamma, start 3] (arXiv:2405.00425)",
      "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": "Sam Azadi, N. D. Drummond, and Sam M. Vinko, Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid, Phys. Rev. B 110, 245145, arXiv:2405.00425, doi:10.1103/PhysRevB.110.245145",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-19",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-19",
        "method": "source text of arXiv:2405.00425 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": "−0.02848(2)",
        "note": "Table IV, Γ start 3, column SJ-DMC; sources/2405.00425.txt line 389; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Table III (txt lines 371-376): the HF energy for the 90-electron square cell at rs=30 and Gamma is printed as -0.0196518 Ha/el. QMBL's own checks/heg-hf/hf.mjs (2 square 45 45 30, Gamma) gives -0.0196517776 (Ewald sum, uniform background, Madelung term included), so Hartree units, per electron and Ewald with Madelung included are fixed by that number. No sentence in the text names the Ewald sum or the Madelung term. Fig. 4 caption (txt line 505) subtracts 'the Madelung energy of a hexagonal lattice, -vM0/rs' from DMC energies, consistent with energies that contain the Madelung term. The Balder",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG2D/square_90_P_45_45_30/",
  "per_site_divisor": 90,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -2.87271,
    "sigma": 0.00009,
    "method": "Fixed-node DMC",
    "method_detail": "Jastrow optimised at Gamma, start 1",
    "reference": "Sam Azadi, N. D. Drummond, and Sam M. Vinko, Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid, Phys. Rev. B 110, 245145, arXiv:2405.00425, doi:10.1103/PhysRevB.110.245145",
    "bound_type": "projected",
    "energy_per_site": -0.031919
  },
  "no_record_reason": null
}