{
  "model": "HEG2D",
  "lattice": "square",
  "n_sites": 114,
  "boundary": "P",
  "params": {
    "N_up": 57,
    "N_dn": 57,
    "rs": 30,
    "twist": "Gamma"
  },
  "instance_id": "HEG2D/square_114_P_57_57_30",
  "rows": [
    {
      "energy": -3.607701,
      "sigma": 0.000456,
      "energy_variance": null,
      "dof": 114,
      "einf": null,
      "v_score": null,
      "method": "Slater-Jastrow",
      "method_detail": "RPA (Gaskell) pseudopotential",
      "method_as_published": "VMC (Slater-Jastrow, RPA pseudopotential)",
      "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": "B. Tanatar & D. M. Ceperley, Ground state of the two-dimensional electron gas, Phys. Rev. B 39, 5005 (1989), doi:10.1103/PhysRevB.39.5005",
      "peer_reviewed": true,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "doi:10.1103/PhysRevB.39.5005: text layer of the publisher PDF (1989 scan), every number checked against the page image at 300 dpi; no LLM transcription of numbers; single reading + page-image check",
        "reported_as": "−0.063293(8)",
        "note": "Table I (normal fluid), row N = 114, column rs = 30; dl/tanatar-ceperley-1989.txt line 166; printed in Ry per electron; matches the page image | Energies in Ry per electron ('Energies in this paper are in units of rydbergs/electron'), converted × 1/2. Ewald sums with each electron's own images ('an electron must also interact with all of its own images which form a square lattice'): the Madelung term is included. Square simulation cell, periodic boundary conditions, plane-wave orbitals filling closed shells (Gamma). QMBL's HF check (checks/heg-hf/hf.mjs, square cell): E - E_HF per electron is -0.099 Ha at N = 26, rs = 1, -0.046 at N = 26, rs = 5, -0.0078 at N = 114, rs = 50, -0.0112 at N = 37 polarized, rs = 5 and -0.0023 at N = 113 polarized, rs = 75, close to the paper's E_c(rs) (Tables I, II); without the Madelung term the N = 26, rs = 1 energy would sit 0.216 Ha per electron higher. Every number checked against the page image (300 dpi).",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/HEG2D/square_114_P_57_57_30/",
  "per_site_divisor": 114,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -3.607701,
    "sigma": 0.000456,
    "method": "Slater-Jastrow",
    "method_detail": "RPA (Gaskell) pseudopotential",
    "reference": "B. Tanatar & D. M. Ceperley, Ground state of the two-dimensional electron gas, Phys. Rev. B 39, 5005 (1989), doi:10.1103/PhysRevB.39.5005",
    "bound_type": "variational",
    "energy_per_site": -0.0316465
  },
  "no_record_reason": null
}