{
  "model": "Heisenberg",
  "lattice": "square",
  "n_sites": 196,
  "boundary": "P",
  "params": {},
  "instance_id": "Heisenberg/square_196_P",
  "rows": [
    {
      "energy": -523.983,
      "sigma": 0.006,
      "energy_variance": 22.07,
      "dof": 196,
      "einf": 0,
      "v_score": 0.0157552032593818,
      "method": "VMC with fermions (flux+neel+Jastrow)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/square_196_P/vmc_gutzwiller.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -516.3911695223306,
      "sigma": null,
      "energy_variance": 127.79517553787447,
      "dof": 100,
      "einf": 0,
      "v_score": 0.04792441769886959,
      "method": "DMRG (bond dimension = 512)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/square_196_P/dmrg.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true,
      "defect": {
        "flag": "dof-mismatch",
        "finding": "Row stores dof = 100 on a 196-site instance. Upstream typo; the V-score derived from it would be wrong by a factor of ~2."
      }
    },
    {
      "energy": -520.4234,
      "sigma": 0.0079,
      "energy_variance": 63.70537,
      "dof": 196,
      "einf": 0,
      "v_score": 0.04610186370257413,
      "method": "RBM (alpha = 1)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/square_196_P/vmc_rbm.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -519.4475,
      "sigma": 0.0081,
      "energy_variance": 66.74661,
      "dof": 196,
      "einf": 0,
      "v_score": 0.04848439309211061,
      "method": "Jastrow baseline",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/square_196_P/vmc_jastrow.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -525.462084,
      "sigma": 0.0000157,
      "energy_variance": null,
      "dof": 196,
      "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 = -0.67023225(2) per spin (S.S), L = 14, 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 = 14. 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_196_P/",
  "per_site_divisor": 784,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -523.983,
    "sigma": 0.006,
    "method": "VMC with fermions (flux+neel+Jastrow)",
    "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/square_196_P/vmc_gutzwiller.sh)",
    "energy_per_site": -0.6683456632653061
  },
  "no_record_reason": null
}