{
  "model": "Hubbard",
  "lattice": "rectangular-4x8",
  "n_sites": 32,
  "boundary": "PO",
  "params": {
    "Nf": 14,
    "U": 8
  },
  "instance_id": "Hubbard/rectangular-4x8_32_PO_14_8",
  "rows": [
    {
      "energy": -23.5645,
      "sigma": null,
      "energy_variance": 0.0155,
      "dof": 28,
      "einf": 49,
      "v_score": 0.0000824216520531738,
      "method": "DMRG (MaxLinkDim = 12000, MaxTruncErr~6.6E-06, extrap energy -23.5658 +/- 0.0003)",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[code](https://github.com/varbench/methods/blob/main/programs/dmrg_itensors_hubbard/rectangular-4x8_32_PO_14_8.jl)",
      "source": "varbench@2024-10-22",
      "provenance": "imported",
      "baseline": true
    },
    {
      "energy": -23.52,
      "sigma": 0.001,
      "energy_variance": 0.035,
      "dof": 28,
      "einf": 49,
      "v_score": 0.00018634188518358406,
      "method": "VMC Hidden Fermion Determinant State Ansatz (N_hidden = 16. Single hidden layer fully connected net with alpha = 14). Soft mean-field constraint for lambda = 8 stripe order.",
      "bound_type": "variational",
      "bound_type_reason": "vmc|\\brbm\\b|\\brnn\\b|jast",
      "reference": "[paper](https://www.pnas.org/doi/full/10.1073/pnas.2122059119)",
      "source": "varbench@2024-10-22",
      "provenance": "imported"
    },
    {
      "energy": -23.46944,
      "sigma": 0.00256,
      "energy_variance": 0.72,
      "dof": 28,
      "einf": 49,
      "v_score": 0.0038386694558110793,
      "method": "Hidden-fermion determinant state (HFDS), 8x4 cylinder",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz; energy is a strict upper bound (assigned during source verification)",
      "reference": "Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model, Phys. Rev. B 113, 245104 (2026), arXiv:2510.11710",
      "peer_reviewed": true,
      "source": "sweep-tables-2026-09-14",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "arXiv HTML parsed locally, no LLM transcription",
        "reported_as": "E_0/M = -0.73342 (+/- 0.00008), sigma^2/M = 0.0225",
        "note": "Read from Table 1 of arXiv:2510.11710 (U/t = 8, n_h = 1/8, energies per site, 131072 samples), parsed from the arXiv HTML. Row \"HFDS (8x4)\".",
        "secondary_of": null
      }
    },
    {
      "energy": -23.4624,
      "sigma": 0.0192,
      "energy_variance": 0.752,
      "dof": 28,
      "einf": 49,
      "v_score": 0.004010056058287358,
      "method": "Jastrow-backflow (JBf), 8x4 cylinder",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz; energy is a strict upper bound (assigned during source verification)",
      "reference": "Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model, Phys. Rev. B 113, 245104 (2026), arXiv:2510.11710",
      "peer_reviewed": true,
      "source": "sweep-tables-2026-09-14",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-09-14",
        "method": "arXiv HTML parsed locally, no LLM transcription",
        "reported_as": "E_0/M = -0.7332 (+/- 0.0006), sigma^2/M = 0.0235",
        "note": "Read from Table 1 of arXiv:2510.11710 (U/t = 8, n_h = 1/8, energies per site, 131072 samples), parsed from the arXiv HTML. Row \"JBf (8x4)\".",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/rectangular-4x8_32_PO_14_8/",
  "per_site_divisor": 32,
  "per_site_label": "E/site",
  "record": {
    "energy": -23.5645,
    "sigma": null,
    "method": "DMRG (MaxLinkDim = 12000, MaxTruncErr~6.6E-06, extrap energy -23.5658 +/- 0.0003)",
    "reference": "[code](https://github.com/varbench/methods/blob/main/programs/dmrg_itensors_hubbard/rectangular-4x8_32_PO_14_8.jl)",
    "energy_per_site": -0.736390625
  },
  "no_record_reason": null
}