{
  "model": "J1J2",
  "lattice": "square",
  "n_sites": 40,
  "boundary": "P",
  "params": {
    "J2": 0.4
  },
  "instance_id": "J1J2/square_40_P_0.4",
  "rows": [
    {
      "energy": -84.3534668,
      "sigma": null,
      "energy_variance": null,
      "dof": 40,
      "einf": 0,
      "v_score": null,
      "method": "Exact diagonalization (Lanczos)",
      "bound_type": "exact",
      "bound_type_reason": "exact diagonalization of the full cluster; deterministic, exact to the printed digits (RULES.md 4)",
      "reference": "Richter & Schulenburg, The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N = 40 spins, Eur. Phys. J. B 73, 117 (2010), arXiv:0909.3723",
      "peer_reviewed": true,
      "source": "exact-2026-09-15",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-15",
        "method": "arXiv PDF extracted locally with pypdf in layout mode, parsed by column position and checked against the paper's own per-site column; no LLM transcription",
        "reported_as": "E_GS(S = 0) = -21.08836670 (total, S.S, J1 = 1), N = 40, J2 = 0.4",
        "note": "Table 1, \"Ground state energy E_GS(S = 0) ...\", row J2 = 0.4. The tilted 40-site square-lattice cluster of the paper's Fig. 1 with periodic boundaries (Sec. 2); E/N = -0.5272092 in S.S units, Pauli total = 4 E. The paper's J2 grid is 0, 0.1, ..., 0.5, 0.55, 0.6, 0.65, 0.7, 0.8, 0.9, 1.0.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/J1J2/square_40_P_0.4/",
  "per_site_divisor": 160,
  "per_site_label": "E/N (S.S)",
  "record": null,
  "no_record_reason": "solved exactly"
}