{
  "model": "Heisenberg",
  "lattice": "square",
  "n_sites": 4096,
  "boundary": "P",
  "params": {},
  "instance_id": "Heisenberg/square_4096_P",
  "rows": [
    {
      "energy": -10968.2805965,
      "sigma": 0.000492,
      "energy_variance": null,
      "dof": 4096,
      "einf": 0,
      "v_score": null,
      "method": "SSE QMC (stochastic series expansion), T -> 0 converged at beta/L = 32 and 64",
      "bound_type": "exact",
      "bound_type_reason": "sign-problem-free SSE QMC on a bipartite lattice, T -> 0 converged; numerically exact (RULES.md 4)",
      "reference": "Sandvik, High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice, arXiv:2601.20189 (2026)",
      "peer_reviewed": false,
      "source": "exact-2026-09-15",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-15",
        "method": "arXiv HTML parsed locally, one value per table cell; no LLM transcription",
        "reported_as": "e0 = -0.66945072(3) per spin (S.S), L = 64, periodic",
        "note": "Table 1, \"Results for different system sizes computed at inverse temperature beta/L = 64 for L > 30 and averaged over beta/L = 32 and beta/L = 64 simulations for L <= 30\", column e0, row L = 64. Pauli total = 4 N e0. The L = 6 value agrees with the exact-diagonalization row on square_36_P to 1.6e-8.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Heisenberg/square_4096_P/",
  "per_site_divisor": 16384,
  "per_site_label": "E/N (S.S)",
  "record": null,
  "no_record_reason": "solved exactly"
}