{ "model": "HEG3D", "lattice": "sc", "n_sites": 14, "boundary": "P", "params": { "N_up": 7, "N_dn": 7, "rs": 20, "twist": "Gamma" }, "instance_id": "HEG3D/sc_14_P_7_7_20", "rows": [ { "energy": -0.4542181, "sigma": 0.0000021, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "WAP-net", "method_detail": "n_d = 1", "method_as_published": "WAP-net (n_d = 1)", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2202.04622 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": "-0.0648883(3)", "note": "Table III column 2 (WAP-Net nd=1), block Ne = 14 (paramagnetic), row rs = 20.0; sources/2202.04622.txt line 521; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.", "secondary_of": null } }, { "energy": -0.4542076, "sigma": 0.0000014, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "WAP-net", "method_detail": "n_d = 8", "method_as_published": "WAP-net (n_d = 8)", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2202.04622 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": "-0.0648868(2)", "note": "Table III column 3 (WAP-Net nd=8), block Ne = 14 (paramagnetic), row rs = 20.0; sources/2202.04622.txt line 521; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.", "secondary_of": null } }, { "energy": -0.4539108, "sigma": 0.0000014, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "Iterative backflow", "method_detail": "single determinant", "method_as_published": "IB-VMC (iterative backflow, single determinant)", "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": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2202.04622 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": "-0.0648444(2)", "note": "Table III column EIBVMC, block Ne = 14 (paramagnetic), row rs = 20.0; sources/2202.04622.txt line 521; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.", "secondary_of": null } }, { "energy": -0.4544099, "sigma": 0.0000035, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "Fixed-node DMC", "method_detail": "trial state: iterative backflow", "method_as_published": "IB-DMC (fixed-node DMC on the iterative-backflow state)", "family": "DMC", "bound_type": "projected", "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)", "reference": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2202.04622 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": "-0.0649157(5)", "note": "Table III column EIBDMC, block Ne = 14 (paramagnetic), row rs = 20.0; sources/2202.04622.txt line 521; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.", "secondary_of": null } }, { "energy": -0.4543742, "sigma": 0.0000028, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "MP-NQS", "method_detail": "plane-wave orbitals", "method_as_published": "MP-NQS (plane-wave orbitals)", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "G. Pescia, J. Nys, J. Kim, A. Lovato & G. Carleo, Message-passing neural quantum states for the homogeneous electron gas, Phys. Rev. B 110, 035108 (2024), arXiv:2305.07240, doi:10.1103/PhysRevB.110.035108", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2305.07240 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": "−0.0324553(2)", "note": "Table I (Appendix G), N=14 unpolarized, rs=20, column MP-NQS; sources/2305.07240.txt line 666; printed in Ha per electron; version read: arXiv text, Appendix G Tables I-V; APS copy not read | Ha per electron, simple cubic cell; Eq. 13 gives the Ewald sum and 'const.'. The WAP-net values it quotes equal arXiv:2202.04622's Table III (Madelung included) / 2 to 5e-7, and its own N = 14, rs = 1 energy sits 0.0376 Ha below QMBL's HF energy, as theirs does.", "secondary_of": null } }, { "energy": -0.45206, "sigma": 0.0000196, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "1 determinant", "method_as_published": "FermiNet (n_det = 1), before basis transformation", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "Liu, Qian & Wang, Enhancing Neural-Network Variational Monte Carlo through Basis Transformation, arXiv:2604.15888", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.15888 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": "-0.45206(2)", "note": "Table III (SM S3.D), rs=20, column E' n_det=1; sources/2604.15888.txt line 1329; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.", "secondary_of": null } }, { "energy": -0.452240000001, "sigma": 0.00000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "1 determinant, Gaussian basis transformation", "method_as_published": "FermiNet (n_det = 1), after basis transformation", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "Liu, Qian & Wang, Enhancing Neural-Network Variational Monte Carlo through Basis Transformation, arXiv:2604.15888", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.15888 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": "-0.45224(1)", "note": "Table III (SM S3.D), rs=20, column E n_det=1; sources/2604.15888.txt line 1329; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.", "secondary_of": null } }, { "energy": -0.452236, "sigma": 0.00000798, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "4 determinants", "method_as_published": "FermiNet (n_det = 4), before basis transformation", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "Liu, Qian & Wang, Enhancing Neural-Network Variational Monte Carlo through Basis Transformation, arXiv:2604.15888", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.15888 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": "-0.452236(8)", "note": "Table III (SM S3.D), rs=20, column E' n_det=4; sources/2604.15888.txt line 1329; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.", "secondary_of": null } }, { "energy": -0.452367, "sigma": 0.00000294, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "4 determinants, Gaussian basis transformation", "method_as_published": "FermiNet (n_det = 4), after basis transformation", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "Liu, Qian & Wang, Enhancing Neural-Network Variational Monte Carlo through Basis Transformation, arXiv:2604.15888", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.15888 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": "-0.452367(3)", "note": "Table III (SM S3.D), rs=20, column E n_det=4; sources/2604.15888.txt line 1329; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.", "secondary_of": null } }, { "energy": -0.45297, "sigma": 0.00000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "16 determinants", "method_as_published": "FermiNet (n_det = 16), before basis transformation", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "Liu, Qian & Wang, Enhancing Neural-Network Variational Monte Carlo through Basis Transformation, arXiv:2604.15888", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.15888 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": "-0.45297(1)", "note": "Table III (SM S3.D), rs=20, column E' n_det=16; sources/2604.15888.txt line 1329; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.", "secondary_of": null } }, { "energy": -0.45304, "sigma": 0.0000406, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "16 determinants, Gaussian basis transformation", "method_as_published": "FermiNet (n_det = 16), after basis transformation", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "Liu, Qian & Wang, Enhancing Neural-Network Variational Monte Carlo through Basis Transformation, arXiv:2604.15888", "peer_reviewed": false, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "source text of arXiv:2604.15888 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": "-0.45304(4)", "note": "Table III (SM S3.D), rs=20, column E n_det=16; sources/2604.15888.txt line 1329; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.", "secondary_of": null } }, { "energy": -0.40936, "sigma": null, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCD", "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCD, complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "source text of arXiv:2103.03176 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": "-0.02924", "note": "Table I, row rs=20.0, column CCD; sources/2103.03176.txt line 382; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.", "secondary_of": null } }, { "energy": -0.4249, "sigma": null, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "DCD", "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "DCD, complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "source text of arXiv:2103.03176 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": "-0.03035", "note": "Table I, row rs=20.0, column DCD; sources/2103.03176.txt line 382; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.", "secondary_of": null } }, { "energy": -0.43904, "sigma": null, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "TC-CCD", "method_detail": "correlator cutoff k_c = 2 × 2π/L; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "TC-CCD (k_c = 2), complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "source text of arXiv:2103.03176 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": "-0.03136", "note": "Table I, row rs=20.0, column TC-CCD; sources/2103.03176.txt line 382; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.", "secondary_of": null } }, { "energy": -0.44814, "sigma": null, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "TC-DCD", "method_detail": "correlator cutoff k_c = 2 × 2π/L; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "TC-DCD (k_c = 2), complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "source text of arXiv:2103.03176 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": "-0.03201", "note": "Table I, row rs=20.0, column TC-DCD; sources/2103.03176.txt line 382; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.", "secondary_of": null } }, { "energy": -0.41832302688, "sigma": 0.00000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "MP2", "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "MP2, complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, A. Grüneis, G. H. Booth, G. Kresse & A. Alavi, Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems, Phys. Rev. B 86, 035111 (2012), arXiv:1202.4990, doi:10.1103/PhysRevB.86.035111", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "source text of arXiv:1202.4990 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": "E_c = -0.09749(1) (total, Ha)", "note": "Table I, rs=20.0; sources/1202.4990.txt line 8301; printed correlation energy -0.09749(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = -0.0229166447771 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table I; APS copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).", "secondary_of": null } }, { "energy": -0.40983302688, "sigma": null, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCD", "method_detail": "full CCD (driver, ladders, rings, crossed-rings, mosaics); equals CCSD in the HEG; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCD [full CCD (driver, ladders, rings, crossed-rings, mosaics); equals CCSD in the HEG; extrapolated: 1/M → 0 (complete basis)] (arXiv:1310.6806)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "James J. Shepherd, Thomas M. Henderson, and Gustavo E. Scuseria, Coupled Cluster Channels in the Homogeneous Electron Gas, J. Chem. Phys. 140, 124102, arXiv:1310.6806, doi:10.1063/1.4867783", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "source text of arXiv:1310.6806 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": "E_c = -0.089", "note": "Table III, rs=20.0, column CCD; sources/1310.6806.txt line 504; printed in Ha, total; printed correlation energy -0.089, E = E_HF + E_c with E_HF = -0.0229166447771 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Sec. II (txt line 64-81): HF eigenvalues with the zero-momentum integral given by 'vM, the Madelung constant ... defined uniquely for a cell geometry and box length, and here we calculate it to be vM L ~ 2.8372'. No Ewald-sum statement beyond that. The paper prints correlation energies only, which do not depend on the Madelung term, and no Hartree-Fock energy.", "secondary_of": null } } ], "url": "https://qmbl.org/i/HEG3D/sc_14_P_7_7_20/", "per_site_divisor": 14, "per_site_label": "E/N (Ha)", "record": { "energy": -0.4544099, "sigma": 0.0000035, "method": "Fixed-node DMC", "method_detail": "trial state: iterative backflow", "reference": "M. Wilson, S. Moroni, M. Holzmann, N. Gao, F. Wudarski, T. Vegge & A. Bhowmik, Neural network ansatz for periodic wave functions and the homogeneous electron gas, Phys. Rev. B 107, 235139 (2023), arXiv:2202.04622, doi:10.1103/PhysRevB.107.235139", "bound_type": "projected", "energy_per_site": -0.032457849999999996 }, "no_record_reason": null }