{
  "model": "Heisenberg",
  "lattice": "triangular",
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  "boundary": "P",
  "params": {},
  "instance_id": "Heisenberg/triangular_1764_P",
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      "einf": 0,
      "v_score": null,
      "method": "ViT",
      "method_detail": "spatial attention, b = 3, translations + C6v projection",
      "method_as_published": "ViT with Spatial Attention, translations + C6v projection",
      "family": "transformer / ViT",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "Viteritti, Rende, Sachdev & Carleo, Approaching the Thermodynamic Limit with Neural-Network Quantum States, arXiv:2602.02665",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:2602.02665 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading, parsed from the committed HTML table and matched against the PDF text",
        "reported_as": "-0.551429(1)",
        "note": "Table 1, 42 × 42 block, row 'ViT', printed '-0.551429(1)', 'This work'; caption: 'The results of this work are obtained by enforcing translational and C6v point-group symmetries (refer to Section V.2)'. | Table 1 prints ground-state energies per site of the spin-1/2 triangular Heisenberg model on periodic L x L clusters (Sec. III: 'All calculations are performed on periodic L x L clusters with L chosen as a multiple of 3', H = J sum S_i.S_j), S.S units. Magnitude check: the values lie between -0.5517 and -0.5520, next to the 12 x 12 value -0.55315 (GCNN, per site, S.S) on Heisenberg/triangular_144_P, not four times it (Pauli) or a total.",
        "secondary_of": null
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      "compute": {
        "parameters": 450000,
        "gpu_hours": 25000,
        "device": "NVIDIA GH200",
        "n_devices": null,
        "samples": 16384,
        "wall_clock": null,
        "cpu_core_hours": null,
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        "iterations": 5600,
        "evaluation": {
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            {
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              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 1
            },
            {
              "iterations": 500,
              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 9
            },
            {
              "iterations": 100,
              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 108
            }
          ],
          "sr": {
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        },
        "reported_as": "The Vision Transformer architecture used in this work comprises h = 12 attention heads, n_l = 8 layers, and an embedding dimension of d = 72, resulting in approximately P ≈ 4.5 × 10^5 trainable parameters for different system sizes, from L = 18 to L = 42. [...] we set b = 3 for the triangular lattice [...] (C6v group for the triangular lattice [...]) [...] Variational Monte Carlo (VMC) optimizations employing M = 2^14 samples for the stochastic estimates were carried out using SR with the linear algebra trick being in the regime P ≫ M enhanced with SPRING. The optimization proceeded in three stages: 5000 steps without symmetry summation, followed by 500 steps including translational symmetries, and a final 100 steps with both rotational and reflection symmetries restored. || Acknowledgments: The numerical experiments performed in this work required 25000 hours on GH200 GPUs.",
        "source": "Sec. V B Architecture and Optimization Details; Acknowledgments, arXiv:2602.02665 (mining pass 2026-09-28)",
        "scope": "paper",
        "confidence": "medium",
        "note": "gpu_hours = 25000 is the total for ALL numerical experiments in the paper (triangular L = 18-42 and the 20x20 J1-J2 run), not for this row. parameters 'approximately 4.5 x 10^5', stated for every triangular size. iterations = 5000 + 500 + 100 stated stages; samples = 2^14 per step. Stages: 1 evaluation per amplitude unsymmetrised; b^2 = 9 translations within a 3x3 patch; those 9 x the 12 C6v elements = 108. sr minsr (the P >> M linear-algebra trick with SPRING)."
      }
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    {
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      "sigma": 0.07056,
      "energy_variance": null,
      "dof": 1764,
      "einf": 0,
      "v_score": null,
      "method": "ViT",
      "method_detail": "spatial attention, b = 3, variance → 0",
      "method_as_published": "ViT with Spatial Attention, zero-variance extrapolation (triangular)",
      "family": "transformer / ViT",
      "bound_type": "extrapolated",
      "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)",
      "reference": "Viteritti, Rende, Sachdev & Carleo, Approaching the Thermodynamic Limit with Neural-Network Quantum States, arXiv:2602.02665",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-09-28",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-28",
        "method": "source text of arXiv:2602.02665 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading, parsed from the committed HTML table and matched against the PDF text",
        "reported_as": "-0.55171(1)",
        "note": "Table 1, 42 × 42 block, row 'Zero Variance', printed '-0.55171(1)', 'This work'; caption: 'For each system size the zero-variance extrapolated energy is also reported'. Sec. V.3 / Fig. 6: linear fit of energy against variance per site over the unprojected, translation-projected and fully projected ViT states at this L; an extrapolation of the same runs, not a separate calculation. | Table 1 prints ground-state energies per site of the spin-1/2 triangular Heisenberg model on periodic L x L clusters (Sec. III: 'All calculations are performed on periodic L x L clusters with L chosen as a multiple of 3', H = J sum S_i.S_j), S.S units. Magnitude check: the values lie between -0.5517 and -0.5520, next to the 12 x 12 value -0.55315 (GCNN, per site, S.S) on Heisenberg/triangular_144_P, not four times it (Pauli) or a total.",
        "secondary_of": null
      },
      "compute": {
        "parameters": 450000,
        "gpu_hours": 25000,
        "device": "NVIDIA GH200",
        "n_devices": null,
        "samples": 16384,
        "wall_clock": null,
        "cpu_core_hours": null,
        "bond_dimension": null,
        "iterations": 5600,
        "evaluation": {
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            {
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              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 1
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            {
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              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 9
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            {
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              "samples": null,
              "parameters": null,
              "evaluations_per_amplitude": 108
            }
          ],
          "sr": {
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        },
        "reported_as": "The Vision Transformer architecture used in this work comprises h = 12 attention heads, n_l = 8 layers, and an embedding dimension of d = 72, resulting in approximately P ≈ 4.5 × 10^5 trainable parameters for different system sizes, from L = 18 to L = 42. [...] we set b = 3 for the triangular lattice [...] (C6v group for the triangular lattice [...]) [...] Variational Monte Carlo (VMC) optimizations employing M = 2^14 samples for the stochastic estimates were carried out using SR with the linear algebra trick being in the regime P ≫ M enhanced with SPRING. The optimization proceeded in three stages: 5000 steps without symmetry summation, followed by 500 steps including translational symmetries, and a final 100 steps with both rotational and reflection symmetries restored. || Acknowledgments: The numerical experiments performed in this work required 25000 hours on GH200 GPUs.",
        "source": "Sec. V B Architecture and Optimization Details; Acknowledgments, arXiv:2602.02665 (mining pass 2026-09-28)",
        "scope": "paper",
        "confidence": "medium",
        "note": "gpu_hours = 25000 is the total for ALL numerical experiments in the paper (triangular L = 18-42 and the 20x20 J1-J2 run), not for this row. parameters 'approximately 4.5 x 10^5', stated for every triangular size. iterations = 5000 + 500 + 100 stated stages; samples = 2^14 per step. Stages: 1 evaluation per amplitude unsymmetrised; b^2 = 9 translations within a 3x3 patch; those 9 x the 12 C6v elements = 108. sr minsr (the P >> M linear-algebra trick with SPRING). This row is the zero-variance extrapolation of the same three stages (Fig. 6), not a separate run, so it draws the same cost again."
      }
    }
  ],
  "url": "https://qmbl.org/i/Heisenberg/triangular_1764_P/",
  "per_site_divisor": 7056,
  "per_site_label": "E/N (S.S)",
  "record": {
    "energy": -3890.883024,
    "sigma": 0.007056,
    "method": "ViT",
    "method_detail": "spatial attention, b = 3, translations + C6v projection",
    "reference": "Viteritti, Rende, Sachdev & Carleo, Approaching the Thermodynamic Limit with Neural-Network Quantum States, arXiv:2602.02665",
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}