{
  "model": "Heisenberg",
  "lattice": "square",
  "n_sites": 36,
  "boundary": "O",
  "params": {},
  "instance_id": "Heisenberg/square_36_O",
  "rows": [
    {
      "energy": -86.9071441699763,
      "sigma": null,
      "energy_variance": null,
      "dof": 36,
      "einf": 0,
      "v_score": null,
      "method": "Exact diagonalization",
      "bound_type": "exact",
      "bound_type_reason": "exact diagonalization|ex",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/square_36_O/ed_lattice_symmetries.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -86.90713263791655,
      "sigma": null,
      "energy_variance": 0.00045932030843687244,
      "dof": 36,
      "einf": 0,
      "v_score": 0.0000021893102276886876,
      "method": "DMRG (bond dimension = 2048)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/square_36_O/dmrg.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -85.4857,
      "sigma": 0.0035,
      "energy_variance": 12.2737,
      "dof": 36,
      "einf": 0,
      "v_score": 0.06046319048946153,
      "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_36_O/vmc_rbm.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -85.6567,
      "sigma": 0.0036,
      "energy_variance": 13.457,
      "dof": 36,
      "einf": 0,
      "v_score": 0.06602798980657479,
      "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_36_O/vmc_jastrow.sh)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -86.907192,
      "sigma": 0.000024,
      "energy_variance": null,
      "dof": 36,
      "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/N_b = 0.3621133(1) (magnitude, per bond, N_b = 60), L = 6, open",
        "note": "Table 2, \"SSE data for L x L systems with open boundary conditions. The ground state energy is normalized by the number of interaction bonds N_b = 2(L^2 - L)\", row L = 6. Printed as a magnitude; E/N = -(E0/N_b) N_b / N = -0.60352217 in S.S units, Pauli total = 4 N E/N. The L = 6 value agrees with the exact-diagonalization row on square_36_O to 3.3e-7 (2 sigma), and L = 10 and 16 reproduce the rows QMBL already quotes from this paper via arXiv:2605.13807.",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Heisenberg/square_36_O/",
  "per_site_divisor": 144,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -86.90713263791655,
    "sigma": null,
    "method": "DMRG (bond dimension = 2048)",
    "reference": "[code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/square_36_O/dmrg.sh)",
    "energy_per_site": -0.603521754429976
  },
  "no_record_reason": null
}