How these numbers were read
Where each number below was read, and how it was checked.
-0.69670(2), VMC (RBM)
Checked 2026-09-14 · arXiv PDF text extracted locally with pypdf, no LLM transcription
Reported as. -0.6967 (+/- 0.00002) per site in S.S units
Read from Table 5 of arXiv:2206.14307 (J1-J2 on 6x6 and 10x10 square lattices, PBC, E/N in S.S units), extracted from the PDF with pypdf.
-0.696641, VMC (ViT)
Checked 2026-09-15 · source text of arXiv:2606.04558 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. -0.696641
Table I, row J2=1.00, column '10×10, ViT (this work)' | Table I value is already printed per-site (not total): e.g. 6×6 ED at J2=0.50 prints -0.503809, exactly matching catalog J1J2/square_36_P_0.5 exact_per_site -0.5038096539; the J2=0.00 quoted QMC column value -0.67349005 [29] exactly equals catalog Heisenberg/square_64_P exact_per_site -0.67349005 (and -0.67155266 [29] equals Heisenberg/square_100_P exact_per_site -0.67155266) — confirms direct S·S per-site match, no Pauli conversion needed.
-0.69636(1), VMC (CNN)
Checked 2026-09-14 · arXiv PDF text extracted locally with pypdf, no LLM transcription
Reported as. -0.69636 (+/- 0.00001) per site in S.S units
Read from Table 5 of arXiv:2206.14307 (J1-J2 on 6x6 and 10x10 square lattices, PBC, E/N in S.S units), extracted from the PDF with pypdf.
-0.69123(1), VMC (Gutzwiller)
Checked 2026-09-15 · source text of arXiv:1903.06713 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. -0.69123(1)
Appendix TABLE I, 10x10 block, row 'VMC', column J2=1.0 | No exact reference; close to current record_eps -0.6967 (RBM wavefunction).
-0.68818(2), VMC (RBM)
Checked 2026-09-29 · scripts/J1J2/square_100_P_1/vmc_rbm.sh + programs/vmc_netket (vmc.py, args_parser.py, ham.py), NetKet 3.13.0 source; varbench/methods@ed31bb0 (shallow clone), VarBench data history (varbench-history, partial clone at 390a21e)
Reported as. python3 vmc.py --ham j1j2 --boundary peri --sign mars --ham_dim 2 --L 10 --J2 1 --zero_mag --net rbm --seed 123 --show_progress
Script builds the 10x10 PBC J1-J2 at J2 = 1 (NetKet Heisenberg, Pauli, J = [1, 1], Marshall rotation on J1 bonds only: isospectral), S^z = 0, MetropolisExchange; nk.models.RBM(alpha = 1, log_cosh) with real float32 parameters; 10^4 SR steps, then a 2^20-sample estimate: stored sigma / sqrt(Var/2^20) = 1.01, i.e. the NetKet error_of_mean of that estimate; variance = Var(H) total. No constant shift in the Hamiltonian (NetKet bond op sz_sz +- exchange), so the M2 gap to the record is the ansatz's: real parameters give positive amplitudes in the Marshall basis. History: entered 6470cd9 (2022-10-18, Dian, 'Add RBM and Jastrow for J1-J2 L=10 scanning J2'); unchanged since; code link added 5047bfd (2024-07-30).
-0.6872611, DMRG
Checked 2026-09-29 · scripts/J1J2/square_100_P_1/dmrg.sh + programs/dmrg_itensors (heisenberg_2d.jl, args.jl, common.jl; ITensors 0.6.16); varbench/methods@ed31bb0 (shallow clone), VarBench data history (varbench-history, partial clone at 390a21e)
Reported as. julia --project heisenberg_2d.jl --peri --L 10 --J2 1 --J22 1 --zero_mag --max_B 1024 --seed 123
Script builds the 10x10 PBC J1-J2 at J2 = J22 = 1 (Pauli, no Marshall rotation, no shift), S^z = 0, max bond dimension 1024 = method string, 50 sweeps, cutoff 1e-12, seed 123; final dmrg() energy: variational at stated bond dimension (no extrapolation), sigma not applicable. D = 1024 on a 10x10 torus is far from converged but is a valid bound at stated bond dimension. History: entered 6e6044e (2022-10-17, Dian, 'Add DMRG for J1-J2 L=10 scanning J2'); unchanged since; code link added f88f9ba (2024-07-19).
-0.64681(3), VMC (Jastrow)
Checked 2026-09-29 · scripts/J1J2/square_100_P_1/vmc_jastrow.sh + programs/vmc_netket (vmc.py, args_parser.py, ham.py), NetKet 3.13.0 source; varbench/methods@ed31bb0 (shallow clone), VarBench data history (varbench-history, partial clone at 390a21e)
Reported as. python3 vmc.py --ham j1j2 --boundary peri --sign mars --ham_dim 2 --L 10 --J2 1 --zero_mag --net jas --seed 123 --show_progress
Script builds the 10x10 PBC J1-J2 at J2 = 1 (NetKet Heisenberg, Pauli, J = [1, 1], Marshall rotation on J1 bonds only: isospectral), S^z = 0, MetropolisExchange; nk.models.Jastrow with real float32 parameters; 10^4 SR steps, then a 2^20-sample estimate: stored sigma / sqrt(Var/2^20) = 1.00, i.e. the NetKet error_of_mean of that estimate; variance = Var(H) total. No constant shift in the Hamiltonian (NetKet bond op sz_sz +- exchange), so the M2 gap to the record is the ansatz's: real parameters give positive amplitudes in the Marshall basis. History: entered 6470cd9 (2022-10-18, Dian, 'Add RBM and Jastrow for J1-J2 L=10 scanning J2'); unchanged since; code link added fdb4bfb (2024-07-30).