{ "model": "Heisenberg", "lattice": "square", "n_sites": "inf", "boundary": "TDL", "params": {}, "instance_id": "Heisenberg/square_inf", "rows": [ { "energy": -2.67768, "sigma": 0.00008, "method": "iPEPS", "method_detail": "fit to D = 3, 4, 5", "method_as_published": "linear fit of iPEPS energy per site vs 1/xi^3 (Eq. 21) using the largest three D values (D = 3, 4, 5), extrapolated xi -> infinity", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "extrapolation in the ansatz", "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:1803.08566: journal version: Phys. Rev. X 8, 031030 (2018), open-access PDF from journals.aps.org (journal/rader-prx.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1803.08566v1 (only version on arXiv; PRX text not downloadable: APS blocks scripted access))); single reading, journal check, second reading 2026-10-25", "reported_as": "e(iPEPS)HB = −0.66942(2)", "note": "Sec. IV.B, text after Fig. 6; line 770 of rader.plain.txt (sources/rader.plain.txt) | per site (energy density e = E/N_sites, stated near Eq. 16; Table B.1 header says only 'Energy /J'); units J; Eq. (23): H_HB = J sum_ (S^x_i S^x_j + S^y_i S^y_j + S^z_i S^z_j), J = 1, S^alpha 'spin 1/2 operators' (as printed), nn bonds | Printed with '≈', no error bar. Paper compares with 'high precision QMC reference values [56, 60]' but does not print the QMC energy in this text. | arXiv v1 printed e_HB ≈ −0.669417; journal p. 10 (journal/rader-prx.plain.txt line 750-751) prints −0.66942(2); the arXiv v1 text printed e_HB ≈ −0.669417 without an error bar", "secondary_of": null } }, { "energy": -2.640924372, "sigma": null, "method": "iPEPS", "method_detail": "D = 2", "method_as_published": "Best variational iPEPS energy (Table B.1)", "bound_type": "variational", "bound_type_reason": "variational state of the infinite system at a fixed ansatz size; energy per site is an upper bound up to the stated contraction (RULES.md 14.4)", "how_tdl": "infinite system", "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:1803.08566: journal version: Phys. Rev. X 8, 031030 (2018), open-access PDF from journals.aps.org (journal/rader-prx.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1803.08566v1 (only version on arXiv; PRX text not downloadable: APS blocks scripted access))); single reading, journal check, second reading 2026-10-25", "reported_as": "−0.660 231 093", "note": "Table B.1 (S = 1/2 HB block); line 1260 of rader.plain.txt (sources/rader.plain.txt) | per site (energy density e = E/N_sites, stated near Eq. 16; Table B.1 header says only 'Energy /J'); units J; Eq. (23): H_HB = J sum_ (S^x_i S^x_j + S^y_i S^y_j + S^z_i S^z_j), J = 1, S^alpha 'spin 1/2 operators' (as printed), nn bonds | Single-site unit cell after sublattice rotation (text before Eq. 23). Digits grouped in threes as printed.", "secondary_of": null } }, { "energy": -2.67189696, "sigma": null, "method": "iPEPS", "method_detail": "D = 3", "method_as_published": "Best variational iPEPS energy (Table B.1)", "bound_type": "variational", "bound_type_reason": "variational state of the infinite system at a fixed ansatz size; energy per site is an upper bound up to the stated contraction (RULES.md 14.4)", "how_tdl": "infinite system", "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:1803.08566: journal version: Phys. Rev. X 8, 031030 (2018), open-access PDF from journals.aps.org (journal/rader-prx.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1803.08566v1 (only version on arXiv; PRX text not downloadable: APS blocks scripted access))); single reading, journal check, second reading 2026-10-25", "reported_as": "−0.667 974 240", "note": "Table B.1 (S = 1/2 HB block); line 1261 of rader.plain.txt (sources/rader.plain.txt) | per site (energy density e = E/N_sites, stated near Eq. 16; Table B.1 header says only 'Energy /J'); units J; Eq. (23): H_HB = J sum_ (S^x_i S^x_j + S^y_i S^y_j + S^z_i S^z_j), J = 1, S^alpha 'spin 1/2 operators' (as printed), nn bonds | Single-site unit cell after sublattice rotation (text before Eq. 23). Digits grouped in threes as printed.", "secondary_of": null } }, { "energy": -2.676335028, "sigma": null, "method": "iPEPS", "method_detail": "D = 4", "method_as_published": "Best variational iPEPS energy (Table B.1)", "bound_type": "variational", "bound_type_reason": "variational state of the infinite system at a fixed ansatz size; energy per site is an upper bound up to the stated contraction (RULES.md 14.4)", "how_tdl": "infinite system", "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:1803.08566: journal version: Phys. Rev. X 8, 031030 (2018), open-access PDF from journals.aps.org (journal/rader-prx.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1803.08566v1 (only version on arXiv; PRX text not downloadable: APS blocks scripted access))); single reading, journal check, second reading 2026-10-25", "reported_as": "−0.669 083 757", "note": "Table B.1 (S = 1/2 HB block); line 1262 of rader.plain.txt (sources/rader.plain.txt) | per site (energy density e = E/N_sites, stated near Eq. 16; Table B.1 header says only 'Energy /J'); units J; Eq. (23): H_HB = J sum_ (S^x_i S^x_j + S^y_i S^y_j + S^z_i S^z_j), J = 1, S^alpha 'spin 1/2 operators' (as printed), nn bonds | Single-site unit cell after sublattice rotation (text before Eq. 23). Digits grouped in threes as printed.", "secondary_of": null } }, { "energy": -2.677512256, "sigma": null, "method": "iPEPS", "method_detail": "D = 5", "method_as_published": "Best variational iPEPS energy (Table B.1)", "bound_type": "variational", "bound_type_reason": "variational state of the infinite system at a fixed ansatz size; energy per site is an upper bound up to the stated contraction (RULES.md 14.4)", "how_tdl": "infinite system", "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:1803.08566: journal version: Phys. Rev. X 8, 031030 (2018), open-access PDF from journals.aps.org (journal/rader-prx.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 1803.08566v1 (only version on arXiv; PRX text not downloadable: APS blocks scripted access))); single reading, journal check, second reading 2026-10-25", "reported_as": "−0.669 378 064", "note": "Table B.1 (S = 1/2 HB block); line 1263 of rader.plain.txt (sources/rader.plain.txt) | per site (energy density e = E/N_sites, stated near Eq. 16; Table B.1 header says only 'Energy /J'); units J; Eq. (23): H_HB = J sum_ (S^x_i S^x_j + S^y_i S^y_j + S^z_i S^z_j), J = 1, S^alpha 'spin 1/2 operators' (as printed), nn bonds | Single-site unit cell after sublattice rotation (text before Eq. 23). Digits grouped in threes as printed.", "secondary_of": null } }, { "energy": -2.677748, "sigma": 0.00002, "method": "SSE QMC", "method_detail": "L = 4-16 (fit L = 6-16)", "method_as_published": "Stochastic series expansion (SSE) QMC, L×L lattices L = 4..16 (L = 4 excluded from fits), fits to polynomials in 1/L constrained by chiral-perturbation / sigma-model scaling forms", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Sandvik, Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model, Phys. Rev. B 56, 11678 (1997), arXiv:cond-mat/9707123", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:cond-mat/9707123: journal version: Phys. Rev. B 56, 11678 (1997), PDF from journals.aps.org over the ETH network (journal/sandvik1997-prb.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: cond-mat/9707123v1)); single reading, journal check, second reading 2026-10-25", "reported_as": "−0.669437(5) (Table III prints 'E -0.669437(5)')", "note": "Table III (parameters from the fully constrained coupled fit, 'taken as the final results'); line Table III, row E; line 790 of sandvik1997.plain.txt of sources/sandvik1997.plain.txt; also abstract line 19 (sources/sandvik1997.plain.txt) | per spin (abstract: 'ground state energy per spin'; Table II header '−E'; N = L×L sites); units J; Eq. (1): H = J sum_ S_i · S_j, (J > 0), S_i spin-1/2 operator, N = L×L sites, pairs of nearest-neighbour sites (each bond once) | Quoted as 'the most accurate estimate reported to date' (1997). Superseded by Sandvik 2026 (-0.669441857(7)); 2026 paper calls them statistically consistent.", "secondary_of": null } }, { "energy": -2.67772, "sigma": 0.00008, "method": "SSE QMC", "method_detail": "L = 4-16 (fit L = 6-16)", "method_as_published": "Stochastic series expansion (SSE) QMC, L×L lattices L = 4..16 (L = 4 excluded from fits), fits to polynomials in 1/L constrained by chiral-perturbation / sigma-model scaling forms", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Sandvik, Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model, Phys. Rev. B 56, 11678 (1997), arXiv:cond-mat/9707123", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:cond-mat/9707123: journal version: Phys. Rev. B 56, 11678 (1997), PDF from journals.aps.org over the ETH network (journal/sandvik1997-prb.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: cond-mat/9707123v1)); single reading, journal check, second reading 2026-10-25", "reported_as": "−0.66943(2)", "note": "Sec. III text, 'Completely independent fits'; line 575 of sources/sandvik1997.plain.txt (sources/sandvik1997.plain.txt) | per spin (abstract: 'ground state energy per spin'; Table II header '−E'; N = L×L sites); units J; Eq. (1): H = J sum_ S_i · S_j, (J > 0), S_i spin-1/2 operator, N = L×L sites, pairs of nearest-neighbour sites (each bond once) | Unconstrained individual fits; intermediate step, not the final result.", "secondary_of": null } }, { "energy": -2.677744, "sigma": 0.00002, "method": "SSE QMC", "method_detail": "L = 4-16 (fit L = 6-16)", "method_as_published": "Stochastic series expansion (SSE) QMC, L×L lattices L = 4..16 (L = 4 excluded from fits), fits to polynomials in 1/L constrained by chiral-perturbation / sigma-model scaling forms", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Sandvik, Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model, Phys. Rev. B 56, 11678 (1997), arXiv:cond-mat/9707123", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:cond-mat/9707123: journal version: Phys. Rev. B 56, 11678 (1997), PDF from journals.aps.org over the ETH network (journal/sandvik1997-prb.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: cond-mat/9707123v1)); single reading, journal check, second reading 2026-10-25", "reported_as": "−0.669436(5)", "note": "Sec. III text, 'partially constrained fit'; line 602 of sources/sandvik1997.plain.txt (sources/sandvik1997.plain.txt) | per spin (abstract: 'ground state energy per spin'; Table II header '−E'; N = L×L sites); units J; Eq. (1): H = J sum_ S_i · S_j, (J > 0), S_i spin-1/2 operator, N = L×L sites, pairs of nearest-neighbour sites (each bond once) | Partially constrained fit (constraint on subleading energy correction not enforced); intermediate step.", "secondary_of": null } }, { "energy": -2.677767428, "sigma": 2.8e-8, "method": "SSE QMC", "method_detail": "L = 6-96 (fit Lmin as noted)", "method_as_published": "SSE QMC, constrained fit (e3, e4 within statistical errors), Lmin = 12", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Sandvik, High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice, J. Stat. Mech. (2026) 043101, arXiv:2601.20189", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:2601.20189: journal version: J. Stat. Mech. (2026) 043101, PDF from iopscience.iop.org over the ETH network (journal/sandvik2026-jsm.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 2601.20189v2 (14 Apr 2026; arXiv comment: 'v2: some errors in Table 1 corrected'))); single reading, journal check, second reading 2026-10-25", "reported_as": "e0 = −0.669441857(7)", "note": "Eq. (23a) / abstract / Sec. on constrained fit; line 1607 of sources/sandvik2026.plain.txt (sources/sandvik2026.plain.txt) | per site (energy density e0); units J; Eq. (1): H = sum_ S_i · S_j, coupling set to unity, nearest-neighbour spins on the square lattice with L×L sites, even L (S_i spin-1/2 as stated in abstract/title) | Final result with fit constrained by chiral-perturbation-theory e3, e4 (Lmin = 12). Also abstract line 17 and line 888. Authors: 'relative statistical error ... 1e-8 and no systematic errors should be expected'.", "secondary_of": null } }, { "energy": -2.677767464, "sigma": 4e-8, "method": "SSE QMC", "method_detail": "L = 6-96 (fit Lmin as noted)", "method_as_published": "SSE QMC, unconstrained fit, Lmin = 8/10", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Sandvik, High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice, J. Stat. Mech. (2026) 043101, arXiv:2601.20189", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:2601.20189: journal version: J. Stat. Mech. (2026) 043101, PDF from iopscience.iop.org over the ETH network (journal/sandvik2026-jsm.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 2601.20189v2 (14 Apr 2026; arXiv comment: 'v2: some errors in Table 1 corrected'))); single reading, journal check, second reading 2026-10-25", "reported_as": "e0 = −0.669441866(10)", "note": "Sec. on extrapolation, unconstrained final; line 858 of sources/sandvik2026.plain.txt (sources/sandvik2026.plain.txt) | per site (energy density e0); units J; Eq. (1): H = sum_ S_i · S_j, coupling set to unity, nearest-neighbour spins on the square lattice with L×L sites, even L (S_i spin-1/2 as stated in abstract/title) | 'the final result of this analysis' of the unconstrained fits (Lmin = 8 and 10 almost identical). The line quoted is the sentence after 'Lmin = 8 and Lmin = 6 ... e0 = −0.669441866(10) and e0 = −0.669441878(9)'.", "secondary_of": null } }, { "energy": -2.67776746, "sigma": 4.4e-8, "method": "SSE QMC", "method_detail": "L = 6-96 (fit Lmin as noted)", "method_as_published": "SSE QMC, unconstrained fit, Lmin = 10", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Sandvik, High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice, J. Stat. Mech. (2026) 043101, arXiv:2601.20189", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:2601.20189: journal version: J. Stat. Mech. (2026) 043101, PDF from iopscience.iop.org over the ETH network (journal/sandvik2026-jsm.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 2601.20189v2 (14 Apr 2026; arXiv comment: 'v2: some errors in Table 1 corrected'))); single reading, journal check, second reading 2026-10-25", "reported_as": "e0 = −0.669441865(11)", "note": "Sec. on extrapolation (Lmin = 10); line 850 of sources/sandvik2026.plain.txt (sources/sandvik2026.plain.txt) | per site (energy density e0); units J; Eq. (1): H = sum_ S_i · S_j, coupling set to unity, nearest-neighbour spins on the square lattice with L×L sites, even L (S_i spin-1/2 as stated in abstract/title) | Unconstrained fit with Lmin = 10.", "secondary_of": null } }, { "energy": -2.677767512, "sigma": 3.6e-8, "method": "SSE QMC", "method_detail": "L = 6-96 (fit Lmin as noted)", "method_as_published": "SSE QMC, unconstrained fit, Lmin = 6", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Sandvik, High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice, J. Stat. Mech. (2026) 043101, arXiv:2601.20189", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:2601.20189: journal version: J. Stat. Mech. (2026) 043101, PDF from iopscience.iop.org over the ETH network (journal/sandvik2026-jsm.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 2601.20189v2 (14 Apr 2026; arXiv comment: 'v2: some errors in Table 1 corrected'))); single reading, journal check, second reading 2026-10-25", "reported_as": "e0 = −0.669441878(9)", "note": "Sec. on extrapolation (Lmin = 6); line 852 of sources/sandvik2026.plain.txt (sources/sandvik2026.plain.txt) | per site (energy density e0); units J; Eq. (1): H = sum_ S_i · S_j, coupling set to unity, nearest-neighbour spins on the square lattice with L×L sites, even L (S_i spin-1/2 as stated in abstract/title) | Unconstrained fit with Lmin = 6 (second value of the pair 'Lmin = 8 ... −0.669441866(10) and Lmin = 6 ... −0.669441878(9)').", "secondary_of": null } }, { "energy": -2.677767444, "sigma": 2.4e-8, "method": "SSE QMC", "method_detail": "L = 6-96 (fit Lmin as noted)", "method_as_published": "SSE QMC, constrained fit, Lmin = 10", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Sandvik, High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice, J. Stat. Mech. (2026) 043101, arXiv:2601.20189", "peer_reviewed": true, "source": "tdl-2026-10-25", "provenance": "primary", "verified": { "checked_on": "2026-10-25", "method": "arXiv:2601.20189: journal version: J. Stat. Mech. (2026) 043101, PDF from iopscience.iop.org over the ETH network (journal/sandvik2026-jsm.pdf), pypdf layout and plain, value found; arXiv text compared (arXiv text (pypdf layout and plain, read locally; version: 2601.20189v2 (14 Apr 2026; arXiv comment: 'v2: some errors in Table 1 corrected'))); single reading, journal check, second reading 2026-10-25", "reported_as": "e0 = −0.669441861(6)", "note": "Sec. on constrained fit (Lmin = 10); line 879 of sources/sandvik2026.plain.txt (sources/sandvik2026.plain.txt) | per site (energy density e0); units J; Eq. (1): H = sum_ S_i · S_j, coupling set to unity, nearest-neighbour spins on the square lattice with L×L sites, even L (S_i spin-1/2 as stated in abstract/title) | Constrained fit, Lmin = 10 (superseded by the Lmin = 12 value taken as final).", "secondary_of": null } }, { "energy": -2.675752, "sigma": 0.000024, "method": "2D minGRU, 3 layers, c4v symmetry, iterative retraining (PSR-NQS)", "method_detail": "fit e(L) = e_inf + a1/L + a2/L^2 + a3/L^3 to the 2D minGRU energies of Table VI, L = 6, 8, ..., 32, 36, 40, 44, 46, 48, 50, 52 (open boundaries)", "method_as_published": "2D minGRU, N = ∞ row of Table VI: 'We perform a fitting using the model e(L) = e_∞ + a1/L + a2/L^2 + a3/L^3 to obtain the thermodynamic limit energy extrapolation of the 2D minGRU and QMC energies'", "bound_type": "extrapolated", "bound_type_reason": "extrapolation to an infinite ansatz or to infinite size; not an upper bound (RULES.md 14.4)", "how_tdl": "finite-size extrapolation", "reference": "Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo, arXiv:2605.13807", "peer_reviewed": false, "source": "tdl-2026-10-27", "provenance": "primary", "verified": { "checked_on": "2026-10-27", "method": "arXiv:2605.13807: arXiv:2605.13807v1 (only version; no journal reference on 2026-10-27): pypdf layout text sources/2605.13807.txt read locally, checked against Table 6 of the arXiv HTML; no LLM transcription; single reading, second reading 2026-10-27 (Table VI, row ∞, column 2D minGRU, line 705 of sources/2605.13807.txt; fit model in the caption)", "reported_as": "−0.668938(6)", "note": "TABLE VI, row N = ∞ (line 703 of sources/2605.13807.txt); fit model in the caption, lines 678-679 | per site in S.S units, J = 1 (the finite-size rows of the same column equal the open-boundary SSE rows of track 1); extrapolation of variational energies, so not an upper bound; the error is the fit's", "secondary_of": null } } ], "url": "https://qmbl.org/instances/#x-Heisenberg_square_inf", "per_site_divisor": 4, "per_site_label": "E/N (S.S)", "best": { "exact": null, "variational": { "energy": -2.677512256, "sigma": null, "method": "iPEPS", "ansatz": null, "method_detail": "D = 5", "reference": "Rader & Läuchli, Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions, Phys. Rev. X 8, 031030 (2018), arXiv:1803.08566", "bound_type": "variational", "energy_per_site": -0.669378064 }, "projected": null, "extrapolated": { "energy": -2.677767512, "sigma": 3.6e-8, "method": "SSE QMC", "ansatz": null, "method_detail": "L = 6-96 (fit Lmin as noted)", "reference": "Sandvik, High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice, J. Stat. Mech. (2026) 043101, arXiv:2601.20189", "bound_type": "extrapolated", "energy_per_site": -0.669441878 }, "approximate": null, "below_exact": [] }, "no_best_reason": null, "record": { "energy": -2.677767512, "sigma": 3.6e-8, "method": "SSE QMC", "ansatz": null, "method_detail": "L = 6-96 (fit Lmin as noted)", "reference": "Sandvik, High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice, J. Stat. Mech. (2026) 043101, arXiv:2601.20189", "bound_type": "extrapolated", "energy_per_site": -0.669441878 }, "no_record_reason": null }