{
  "model": "Heisenberg",
  "lattice": "square",
  "n_sites": 2704,
  "boundary": "O",
  "params": {},
  "instance_id": "Heisenberg/square_2704_O",
  "rows": [
    {
      "energy": -7149.019072,
      "sigma": 0.043264,
      "energy_variance": null,
      "dof": 2704,
      "einf": 0,
      "v_score": null,
      "method": "VMC",
      "ansatz": "minGRU",
      "method_detail": "3 layers, d_h = 256, b = 2, iterative retraining; symmetric: C4v",
      "method_as_published": "2D minGRU, 3 layers, c4v symmetry, iterative retraining (PSR-NQS)",
      "family": "RNN",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo, arXiv:2605.13807",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-27",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-27",
        "method": "arXiv:2605.13807: arXiv:2605.13807v1 (only version; no journal reference on 2026-10-27): pypdf layout text sources/2605.13807.txt read locally, checked against Table 6 of the arXiv HTML sources/2605.13807.html; no LLM transcription; single reading",
        "reported_as": "-0.660967(4)",
        "note": "TABLE VI, row N = 52^2 (line 702 of sources/2605.13807.txt) | energy per site in S.S units, J = 1, open boundaries (caption: '2D Heisenberg model with OBC'); same convention as the table's QMC column, which equals the stored SSE rows at every size it covers; the table prints no QMC value at this size",
        "secondary_of": null
      },
      "compute": {
        "parameters": 800000,
        "gpu_hours": null,
        "device": "NVIDIA A100 80GB",
        "n_devices": 1,
        "samples": 200,
        "wall_clock": "582:41:16 cumulative training time (hh:mm:ss) from 6x6 up to and including 52x52; 405.6 s per training step at 52x52",
        "cpu_core_hours": null,
        "bond_dimension": null,
        "iterations": 502,
        "evaluation": {
          "evaluations_per_amplitude": 8,
          "proposals_per_sample": 1,
          "local_energy": "all",
          "complex": false,
          "sr": {
            "kind": "none"
          },
          "code": "PSR-NQS @ f32468c (JAX, float32)"
        },
        "reported_as": "TABLE VI caption: '...We also report our runtimes for training the 2D minGRU using a single A100 80GB GPU. For reference, this PSR-NQS model has around 800,000 variational parameters.' || TABLE VI row N = 52^2: Time per training step (s) 405.6; Training steps 502; Cumulative training time 582:41:16 || TABLE V: Number of samples (train) 200",
        "source": "Table VI (row and caption) and Table V, arXiv:2605.13807",
        "scope": "row",
        "confidence": "high",
        "note": "iterations = this size's training steps; wall_clock is cumulative over all sizes from 6x6 (iterative retraining), not this size alone. samples = 200 training samples per step (Table V); final energies use 100000 samples. The paper-wide 1400 GPU-hour budget (Sec. V) is not attributed to this row. evaluation as on the 10x10 and 16x16 rows of the same table (single c4v stage at L > 6, run_iterative.py @ f32468c)."
      }
    }
  ],
  "url": "https://qmbl.org/i/Heisenberg/square_2704_O/",
  "per_site_divisor": 10816,
  "per_site_label": "E/N (S.S)",
  "best": {
    "exact": null,
    "variational": {
      "energy": -7149.019072,
      "sigma": 0.043264,
      "method": "VMC",
      "ansatz": "minGRU",
      "method_detail": "3 layers, d_h = 256, b = 2, iterative retraining; symmetric: C4v",
      "reference": "Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo, arXiv:2605.13807",
      "bound_type": "variational",
      "energy_per_site": -0.660967
    },
    "projected": null,
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -7149.019072,
    "sigma": 0.043264,
    "method": "VMC",
    "ansatz": "minGRU",
    "method_detail": "3 layers, d_h = 256, b = 2, iterative retraining; symmetric: C4v",
    "reference": "Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo, arXiv:2605.13807",
    "bound_type": "variational",
    "energy_per_site": -0.660967
  },
  "no_record_reason": null
}