{ "model": "Hubbard", "lattice": "square", "n_sites": 256, "boundary": "P", "params": { "Nf": 112, "U": 8, "t1": 1, "t2": -0.2 }, "instance_id": "Hubbard/square_256_P_112_8_t12_-0.2", "rows": [ { "energy": -187.9552, "sigma": 0.0512, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Tensor backflow", "method_detail": "pinning field PF1 in the optimisation only, UHF orbitals at U = 4, 2484 steps after its removal", "method_as_published": "Tensor backflow (p = 0, PF1, U_UHF = 4, 2484 steps)", "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": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2609.22618 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": "-0.7342(2)", "note": "TABLE III, row E_p=0, column 1 (PF1, U_UHF=4, steps=2484); sources/2609.22618.txt line 406; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.", "secondary_of": null } }, { "energy": -189.3376, "sigma": 0.0256, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Tensor backflow", "method_detail": "pinning field PF1 in the optimisation only, UHF orbitals at U = 4, 2484 steps after its removal, 1 Lanczos step", "method_as_published": "Tensor backflow (p = 1, PF1, U_UHF = 4, 2484 steps)", "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": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2609.22618 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": "-0.7396(1)", "note": "TABLE III, row E_p=1, column 1 (PF1, U_UHF=4, steps=2484); sources/2609.22618.txt line 407; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.", "secondary_of": null } }, { "energy": -188.1856, "sigma": 0.0512, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Tensor backflow", "method_detail": "pinning field PF2 in the optimisation only, UHF orbitals at U = 4, 2152 steps after its removal", "method_as_published": "Tensor backflow (p = 0, PF2, U_UHF = 4, 2152 steps)", "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": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2609.22618 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": "-0.7351(2)", "note": "TABLE III, row E_p=0, column 2 (PF2, U_UHF=4, steps=2152); sources/2609.22618.txt line 406; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.", "secondary_of": null } }, { "energy": -189.44, "sigma": 0.0256, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Tensor backflow", "method_detail": "pinning field PF2 in the optimisation only, UHF orbitals at U = 4, 2152 steps after its removal, 1 Lanczos step", "method_as_published": "Tensor backflow (p = 1, PF2, U_UHF = 4, 2152 steps)", "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": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2609.22618 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": "-0.7400(1)", "note": "TABLE III, row E_p=1, column 2 (PF2, U_UHF=4, steps=2152); sources/2609.22618.txt line 407; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.", "secondary_of": null } }, { "energy": -188.1344, "sigma": 0.1792, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Tensor backflow", "method_detail": "pinning field PF2 in the optimisation only, UHF orbitals at U = 0, 2020 steps after its removal", "method_as_published": "Tensor backflow (p = 0, PF2, U_UHF = 0, 2020 steps)", "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": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2609.22618 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": "-0.7349(7)", "note": "TABLE III, row E_p=0, column 3 (PF2, U_UHF=0, steps=2020); sources/2609.22618.txt line 406; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.", "secondary_of": null } }, { "energy": -189.4656, "sigma": 0.0512, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Tensor backflow", "method_detail": "pinning field PF3 in the optimisation only, UHF orbitals at U = 4, 1925 steps after its removal, 1 Lanczos step", "method_as_published": "Tensor backflow (p = 1, PF3, U_UHF = 4, 1925 steps)", "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": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2609.22618 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": "-0.7401(2)", "note": "TABLE III, row E_p=1, column 4 (PF3, U_UHF=4, steps=1925); sources/2609.22618.txt line 407; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.", "secondary_of": null } }, { "energy": -188.416, "sigma": 0.1792, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Tensor backflow", "method_detail": "pinning field PF3 in the optimisation only, UHF orbitals at U = 4, 9013 steps after its removal", "method_as_published": "Tensor backflow (p = 0, PF3, U_UHF = 4, 9013 steps)", "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": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2609.22618 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": "-0.7360(7)", "note": "TABLE III, row E_p=0, column 5 (PF3, U_UHF=4, steps=9013); sources/2609.22618.txt line 406; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.", "secondary_of": null } }, { "energy": -189.6448, "sigma": 0.0256, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Tensor backflow", "method_detail": "pinning field PF3 in the optimisation only, UHF orbitals at U = 4, 9013 steps after its removal, 1 Lanczos step", "method_as_published": "Tensor backflow (p = 1, PF3, U_UHF = 4, 9013 steps)", "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": "X. Liang, Probing d-wave pairing in the t-t'-U Hubbard model with tensor-backflow wave functions, arXiv:2609.22618", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2609.22618 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": "-0.7408(1)", "note": "TABLE III, row E_p=1, column 5 (PF3, U_UHF=4, steps=9013); sources/2609.22618.txt line 407; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.", "secondary_of": null } }, { "energy": -190.49216, "sigma": 0.00256, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "SBP", "method_detail": "symmetric: unspecified", "method_as_published": "SBP (symmetry-preserving backflow-Pfaffian)", "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": "R. Rende, L. L. Viteritti & A. Georges, Superconductivity in the t-t' Hubbard Model from Symmetry-Preserving Neural-Network Quantum States, arXiv:2608.12465", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2608.12465 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": "-0.74411(1)", "note": "TABLE I (Ground-state variational energies and variances per site, PBC, t'=-0.2, U=8, delta=1/8), 16x16 / SBP; sources/2608.12465.txt line 298; version read: arXiv v1 (sources/2608.12465.txt); no journal version (Crossref, arXiv abs page) | Eq. (1): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t' = -0.2, U = 8, doping 1/8, L x L periodic; Table I: energies and variances per site.", "secondary_of": null } }, { "energy": -188.7488, "sigma": null, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "SCALE", "method_detail": "1 conv layer", "method_as_published": "SCALE (1 conv layer), no symmetry projection", "family": "CNN / ResNet", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.25775 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": "-0.7373", "note": "Table I (16x16 Hubbard, U=8 and delta=1/8 per Sec. III C text; caption prints neither); columns t'=0 OBC | t'=0 PBC | t'=-0.2 PBC; row SCALE, column t'=-0.2 PBC; sources/2604.25775.txt line 478; version read: arXiv v1 (sources/2604.25775.txt); APS copy not reached (403, 2026-10-16) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, U = 8, doping 1/8 (Sec. III), periodic unless the column says OBC; energies per site. Pinning fields only in pre-training (App. C).", "secondary_of": null } }, { "energy": -189.568, "sigma": null, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Fixed-node GFMC", "method_detail": "trial state: SCALE, 1 conv layer", "method_as_published": "SCALE (1 conv layer) trial state + fixed-node GFMC", "family": "AFQMC / GFMC", "bound_type": "projected", "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)", "reference": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.25775 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": "-0.7405", "note": "Table I (16x16 Hubbard, U=8 and delta=1/8 per Sec. III C text; caption prints neither); columns t'=0 OBC | t'=0 PBC | t'=-0.2 PBC; row SCALE+GFMC, column t'=-0.2 PBC; sources/2604.25775.txt line 479; version read: arXiv v1 (sources/2604.25775.txt); APS copy not reached (403, 2026-10-16) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, U = 8, doping 1/8 (Sec. III), periodic unless the column says OBC; energies per site. Pinning fields only in pre-training (App. C).", "secondary_of": null } }, { "energy": -190.208, "sigma": null, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "ACE", "method_detail": "16 conv layers", "method_as_published": "ACE (16 conv layers), no symmetry projection", "family": "CNN / ResNet", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.25775 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": "-0.7430", "note": "Table I (16x16 Hubbard, U=8 and delta=1/8 per Sec. III C text; caption prints neither); columns t'=0 OBC | t'=0 PBC | t'=-0.2 PBC; row ACE, column t'=-0.2 PBC; sources/2604.25775.txt line 480; version read: arXiv v1 (sources/2604.25775.txt); APS copy not reached (403, 2026-10-16) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, U = 8, doping 1/8 (Sec. III), periodic unless the column says OBC; energies per site. Pinning fields only in pre-training (App. C).", "secondary_of": null } }, { "energy": -190.464, "sigma": null, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "Fixed-node GFMC", "method_detail": "trial state: ACE", "method_as_published": "ACE+GFMC (GFMC projection on the ACE trial state)", "family": "AFQMC / GFMC", "bound_type": "projected", "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)", "reference": "Y. Gu, Z. Han, W. Li, Z. Xiao, T. Xiang, M. Qin, L. Wang & D. Lv, Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions, PRX Intelligence 1, 023001 (2026), arXiv:2604.25775, doi:10.1103/2kq2-5g5q", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.25775 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": "-0.7440", "note": "Table I (16x16 Hubbard, U=8 and delta=1/8 per Sec. III C text; caption prints neither); columns t'=0 OBC | t'=0 PBC | t'=-0.2 PBC; row ACE+GFMC, column t'=-0.2 PBC; sources/2604.25775.txt line 481; version read: arXiv v1 (sources/2604.25775.txt); APS copy not reached (403, 2026-10-16) | Eq. (8): H = -t sum_ - t' sum_<> + U sum n_up n_dn, t = 1, U = 8, doping 1/8 (Sec. III), periodic unless the column says OBC; energies per site. Pinning fields only in pre-training (App. C).", "secondary_of": null } }, { "energy": -185.8816, "sigma": 0.0256, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "HFPS", "method_detail": "filled stripe", "method_as_published": "HFPS (filled stripe, Table V)", "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-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "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": "-0.7261(1)", "note": "Table V (App. D 'Supplementary data': 256-site 16x16 cluster, U=8, delta=1/8; columns Filled Stripe | Half-filled stripe + No SC | Half-filled stripe + SC); row t'=-0.2, column Filled Stripe; sources/2511.07566.txt line 1196; 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": -188.416, "sigma": 0.0256, "energy_variance": null, "dof": 224, "einf": 392, "v_score": null, "method": "HFPS", "method_detail": "half-filled stripe + d-wave superconductivity", "method_as_published": "HFPS (half-filled stripe + SC, Table V)", "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-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "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": "-0.7360(1)", "note": "Table V (App. D 'Supplementary data': 256-site 16x16 cluster, U=8, delta=1/8; columns Filled Stripe | Half-filled stripe + No SC | Half-filled stripe + SC); row t'=-0.2, column Half-filled stripe + SC; sources/2511.07566.txt line 1196; 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_256_P_112_8_t12_-0.2/", "per_site_divisor": 256, "per_site_label": "E/site", "record": { "energy": -190.49216, "sigma": 0.00256, "method": "SBP", "method_detail": "symmetric: unspecified", "reference": "R. Rende, L. L. Viteritti & A. Georges, Superconductivity in the t-t' Hubbard Model from Symmetry-Preserving Neural-Network Quantum States, arXiv:2608.12465", "bound_type": "variational", "energy_per_site": -0.74411 }, "no_record_reason": null }