{
  "model": "Hubbard",
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  "boundary": "P",
  "params": {
    "Nf": 60,
    "U": 4
  },
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        "reported_as": "-1.0717(2)",
        "note": "Table II (144-site 12x12 cluster, delta=1/6, U=4, t'=0; columns Delta_0 | U_0 | E/N | C_p | Phase); row Delta_0=0.0, U_0=1; sources/2511.07566.txt line 371; version read: arXiv v1 (sources/2511.07566.txt); no journal version (Crossref, arXiv abs page) | Eq. (1): H = U sum n_up n_dn - sum t_xx' c+c, t_xx' = t' on next-nearest bonds, periodic; Table V: 16x16, U = 8, doping 1/8, energy per site. The d-wave field Delta_0 enters only the mean-field Hamiltonian of the initial orbitals (Eq. 5, App. D).",
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      "reference": "C. Roth, A. Chen, A. Sengupta & A. Georges, Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states, arXiv:2511.07566",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2511.07566 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
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        "note": "Table II (144-site 12x12 cluster, delta=1/6, U=4, t'=0; columns Delta_0 | U_0 | E/N | C_p | Phase); row Delta_0=0.2, U_0=3; sources/2511.07566.txt line 372; version read: arXiv v1 (sources/2511.07566.txt); no journal version (Crossref, arXiv abs page) | Eq. (1): H = U sum n_up n_dn - sum t_xx' c+c, t_xx' = t' on next-nearest bonds, periodic; Table V: 16x16, U = 8, doping 1/8, energy per site. The d-wave field Delta_0 enters only the mean-field Hamiltonian of the initial orbitals (Eq. 5, App. D).",
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      "method_detail": "GCNN; initialised at Δ0 = 0.5, U0 = 3; d-wave superconductor",
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      "family": "backflow / Pfaffian",
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      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "C. Roth, A. Chen, A. Sengupta & A. Georges, Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states, arXiv:2511.07566",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
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        "method": "source text of arXiv:2511.07566 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-1.0751(1)",
        "note": "Table II (144-site 12x12 cluster, delta=1/6, U=4, t'=0; columns Delta_0 | U_0 | E/N | C_p | Phase); row Delta_0=0.5, U_0=3; sources/2511.07566.txt line 373; version read: arXiv v1 (sources/2511.07566.txt); no journal version (Crossref, arXiv abs page) | Eq. (1): H = U sum n_up n_dn - sum t_xx' c+c, t_xx' = t' on next-nearest bonds, periodic; Table V: 16x16, U = 8, doping 1/8, energy per site. The d-wave field Delta_0 enters only the mean-field Hamiltonian of the initial orbitals (Eq. 5, App. D).",
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      "v_score": null,
      "method": "HFPS",
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      "family": "backflow / Pfaffian",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "C. Roth, A. Chen, A. Sengupta & A. Georges, Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states, arXiv:2511.07566",
      "peer_reviewed": false,
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      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2511.07566 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-1.0743(1)",
        "note": "Table II (144-site 12x12 cluster, delta=1/6, U=4, t'=0; columns Delta_0 | U_0 | E/N | C_p | Phase); row Delta_0=1.0, U_0=3; sources/2511.07566.txt line 374; version read: arXiv v1 (sources/2511.07566.txt); no journal version (Crossref, arXiv abs page) | Eq. (1): H = U sum n_up n_dn - sum t_xx' c+c, t_xx' = t' on next-nearest bonds, periodic; Table V: 16x16, U = 8, doping 1/8, energy per site. The d-wave field Delta_0 enters only the mean-field Hamiltonian of the initial orbitals (Eq. 5, App. D).",
        "secondary_of": null
      }
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      "energy_variance": null,
      "dof": 120,
      "einf": 100,
      "v_score": null,
      "method": "HFPS",
      "method_detail": "GCNN; initialised at Δ0 = 0.0, U0 = 3; stripe",
      "method_as_published": "HFPS + GCNN (initialised at Δ0 = 0.0, U0 = 3; stripe, Table II)",
      "family": "backflow / Pfaffian",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "C. Roth, A. Chen, A. Sengupta & A. Georges, Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states, arXiv:2511.07566",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2511.07566 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-1.0700(2)",
        "note": "Table II (144-site 12x12 cluster, delta=1/6, U=4, t'=0; columns Delta_0 | U_0 | E/N | C_p | Phase); row Delta_0=0.0, U_0=3; sources/2511.07566.txt line 375; version read: arXiv v1 (sources/2511.07566.txt); no journal version (Crossref, arXiv abs page) | Eq. (1): H = U sum n_up n_dn - sum t_xx' c+c, t_xx' = t' on next-nearest bonds, periodic; Table V: 16x16, U = 8, doping 1/8, energy per site. The d-wave field Delta_0 enters only the mean-field Hamiltonian of the initial orbitals (Eq. 5, App. D).",
        "secondary_of": null
      }
    },
    {
      "energy": -154.81152,
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      "energy_variance": null,
      "dof": 120,
      "einf": 100,
      "v_score": null,
      "method": "HFPS",
      "method_detail": "GCNN; lowest energy over the initialisations tried",
      "method_as_published": "HFPS + GCNN (lowest-energy state, Table VII)",
      "family": "backflow / Pfaffian",
      "bound_type": "variational",
      "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)",
      "reference": "C. Roth, A. Chen, A. Sengupta & A. Georges, Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states, arXiv:2511.07566",
      "peer_reviewed": false,
      "source": "sweep-allresults-2026-10-22",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-22",
        "method": "source text of arXiv:2511.07566 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading",
        "reported_as": "-1.07508(4)",
        "note": "Table VII (App. D, lowest-energy wavefunction on the 144-site cluster at various U; t'=0, delta=1/6 from Fig. 4 caption and Sec. IV C); row U=4; sources/2511.07566.txt line 1224; version read: arXiv v1 (sources/2511.07566.txt); no journal version (Crossref, arXiv abs page) | Eq. (1): H = U sum n_up n_dn - sum t_xx' c+c, t_xx' = t' on next-nearest bonds, periodic; Table V: 16x16, U = 8, doping 1/8, energy per site. The d-wave field Delta_0 enters only the mean-field Hamiltonian of the initial orbitals (Eq. 5, App. D).",
        "secondary_of": null
      }
    }
  ],
  "url": "https://qmbl.org/i/Hubbard/square_144_P_60_4/",
  "per_site_divisor": 144,
  "per_site_label": "E/site",
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    "reference": "C. Roth, A. Chen, A. Sengupta & A. Georges, Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states, arXiv:2511.07566",
    "bound_type": "variational",
    "energy_per_site": -1.0751
  },
  "no_record_reason": null
}