{
  "model": "Heisenberg",
  "lattice": "pyrochlore-4x4x4",
  "n_sites": 256,
  "boundary": "P",
  "params": {},
  "instance_id": "Heisenberg/pyrochlore-4x4x4_256_P",
  "rows": [
    {
      "energy": -494.69,
      "sigma": 0.076,
      "energy_variance": 109.41,
      "dof": 256,
      "einf": 0,
      "v_score": 0.11445393291700551,
      "method": "mVMC with SU(2) and symmetry projections",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[paper](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.041021)",
      "source": "varbench@2024-10-22",
      "provenance": "imported"
    },
    {
      "energy": -497.152,
      "sigma": null,
      "energy_variance": null,
      "dof": 256,
      "einf": 0,
      "v_score": null,
      "method": "Generalized RVB ansatz, unrestricted VMC optimization (no quantum-number projection)",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz; energy is a strict upper bound (assigned during source verification)",
      "reference": "Closely competing valence bond crystal orders in the ground state of the spin-1/2 antiferromagnetic Heisenberg model on the pyrochlore lattice: a large scale unrestricted variational study, arXiv:2509.13746",
      "peer_reviewed": false,
      "source": "sweep-worklist-2026-09-15",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-15",
        "method": "arXiv PDF text extracted locally with pypdf in layout mode, no LLM transcription",
        "reported_as": "E0 ~ -0.4855 J/site, approximate, no error bar",
        "note": "Sec. A: \"The obtained ground state energy is E0 ~ -0.5118 J/site for the L = 2 cluster and E0 ~ -0.4855 J/site for the L = 4 cluster\", periodic boundary conditions on both; the L = 4 cluster carries Nv = 4N^2 = 262144 parameters, so N = 256. Units: the same passage quotes the mVMC energy -0.5162 J/site for L = 2, which is the pyrochlore-2x2x2_32_P record -0.516266 in the S.S per-site convention. Approximate and without an error bar, so it is eligible for nothing (RULES.md 6). It is nonetheless 0.5% below the VarBench mVMC record -0.4830957, although the ansatz has no symmetry projection and sits above mVMC at L = 2 - which says more about that record than about this row.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Heisenberg/pyrochlore-4x4x4_256_P/",
  "per_site_divisor": 1024,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -494.69,
    "sigma": 0.076,
    "method": "mVMC with SU(2) and symmetry projections",
    "reference": "[paper](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.041021)",
    "energy_per_site": -0.483095703125
  },
  "no_record_reason": null
}