How these numbers were read
Where each number below was read, and how it was checked.
-0.5108232, DMRG
Checked 2026-09-29 · VarBench snapshot 390a21e (vendor/varbench) and full upstream history (varbench-history, git log --follow on the file, every version); varbench/methods ed31bb0 run script and program read as text; no output log or result file exists in the methods repo for any Heisenberg row
Reported as. | -400.485387 | | 93.7656 | 196 | 0 | DMRG (Bond dimension = 2000) | [code](https://github.com/varbench/methods/blob/main/programs/dmrg_itensor_cpp/dmrg_triangular_heisenberg_14x14.cc) |
Program dmrg_triangular_heisenberg_14x14.cc (M. Hibat-Allah, ITensor C++): 14x14 triangularLattice, YPeriodic=false (open), H = sum S.S (printed in S.S units), Neel start with QN conservation (Sz = 0), maxdim schedule ending at 2000, cutoff 1e-10: final energy, variational. Stored = 4 x -100.12134675. arXiv:2207.14314 used D = 2000 at 14x14. Same caveat as the 12x12 program: the variance lines do not compile, so the stored 93.7656 has no runnable source (consistent with Pauli: below the Julia D = 1024 row in both energy and variance). History: -99.64593 (S.S, 1bf1095, 2022-02-15) -> x4 -398.58372 (878bf7a) -> -400.485387 with variance 93.7656 (27c25da, 2023-02-01, Hibat-Allah): a new run. 2.319 above the gated-RNN record. Linked 9369b7d (2024-08-13).
-0.5104501, DMRG
Checked 2026-09-29 · VarBench snapshot 390a21e (vendor/varbench) and full upstream history (varbench-history, git log --follow on the file, every version); varbench/methods ed31bb0 run script and program read as text; no output log or result file exists in the methods repo for any Heisenberg row
Reported as. | -400.1928613876728 | | 113.97946098516695 | 196 | 0 | DMRG (bond dimension = 1024) | [code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/triangular_196_O/dmrg.sh) |
dmrg.sh first line: heisenberg_2d.jl --L 14 --J2 1 --zero_mag --max_B 1024: open 14x14 triangular rhombus, Pauli, J = 1, Sz = 0, 50 sweeps at D = 1024. 0.293 above the C++ D = 2000 row. Entered 3c108e3 (2022-07-11, Dian Wu), never changed; linked 2024-07-19.
-0.47794(2), VMC (RBM)
Checked 2026-09-29 · VarBench snapshot 390a21e (vendor/varbench) and full upstream history (varbench-history, git log --follow on the file, every version); varbench/methods ed31bb0 run script and program read as text; no output log or result file exists in the methods repo for any Heisenberg row
Reported as. | -374.707 | 0.015 | 228.613 | 196 | 0 | RBM (alpha = 1) | [code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/triangular_196_O/vmc_rbm.sh) |
scripts/Heisenberg/triangular_196_O/vmc_rbm.sh: 'python3 vmc.py --ham heis_tri --boundary open --sign mars --ham_dim 2 --L 14 --zero_mag --net rbm --seed 123 --show_progress' -> 14x14 triangular lattice (ColoredJ1J2 back_diag=False: square grid + (i,j)-(i+1,j+1) diagonals), open; NetKet Heisenberg J = 1 in Pauli form with Marshall rotation on the square bonds only (sign_rule=[True, False], a unitary: the diagonals join same-sublattice sites); Sz = 0 (total_sz=0, MetropolisExchange); real float32 RBM, alpha = 1 (nk.models.RBM, log_cosh); 10^4 SR steps; final estimate over 2^20 samples (vmc.py lines 268-269). sigma/sqrt(Var/2^20) = 1.016: the stored sigma is the error of that final estimate. 28.0970 above the 2D gated RNN record -402.804(76). M2/M6 flags (if any): real float32 parameters make the amplitudes positive, so on this frustrated lattice the ansatz cannot carry the ground-state signs; no constant shift is involved and the energy is a valid bound. History: entered 10f5c12 (2022-07-11, Dian Wu) as -373.638 | 0.016 | 258.142 | RBM (alpha = 1); af1d48f (2022-09-01, 'Add Jastrow baseline'): energy -373.638 -> -373.709; variance 258.142 -> 261.002; 59e621a (2022-09-13, 'Update Jastrow and RBM baselines'): energy -373.709 -> -374.707; sigma 0.016 -> 0.015; variance 261.002 -> 228.613; linked 5047bfd (2024-07-30). The first value change sits in af1d48f, titled 'Add Jastrow baseline'. Program files postdate the value (scripts added to varbench/methods 2024-07-30); they document the settings after the run.
-0.47640(2), VMC (Jastrow)
Checked 2026-09-29 · VarBench snapshot 390a21e (vendor/varbench) and full upstream history (varbench-history, git log --follow on the file, every version); varbench/methods ed31bb0 run script and program read as text; no output log or result file exists in the methods repo for any Heisenberg row
Reported as. | -373.499 | 0.013 | 177.484 | 196 | 0 | Jastrow baseline | [code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/triangular_196_O/vmc_jastrow.sh) |
scripts/Heisenberg/triangular_196_O/vmc_jastrow.sh: 'python3 vmc.py --ham heis_tri --boundary open --sign mars --ham_dim 2 --L 14 --zero_mag --net jas --seed 123 --show_progress' -> 14x14 triangular lattice (ColoredJ1J2 back_diag=False: square grid + (i,j)-(i+1,j+1) diagonals), open; NetKet Heisenberg J = 1 in Pauli form with Marshall rotation on the square bonds only (sign_rule=[True, False], a unitary: the diagonals join same-sublattice sites); Sz = 0 (total_sz=0, MetropolisExchange); real float32 Jastrow (nk.models.Jastrow); 10^4 SR steps; final estimate over 2^20 samples (vmc.py lines 268-269). sigma/sqrt(Var/2^20) = 0.999: the stored sigma is the error of that final estimate. 29.3050 above the 2D gated RNN record -402.804(76). M2/M6 flags (if any): real float32 parameters make the amplitudes positive, so on this frustrated lattice the ansatz cannot carry the ground-state signs; no constant shift is involved and the energy is a valid bound. History: entered af1d48f (2022-09-01, Dian Wu) as -366.93763 | 0.014 | 195.304 | Jastrow baseline; 59e621a (2022-09-13, 'Update Jastrow and RBM baselines'): energy -366.93763 -> -373.499; sigma 0.014 -> 0.013; variance 195.304 -> 177.484; linked fdb4bfb (2024-07-30). Program files postdate the value (scripts added to varbench/methods 2024-07-30); they document the settings after the run.