How these numbers were read
Where each number below was read, and how it was checked.
-0.6862(2), CP-AFQMC (stripe)
Checked 2026-10-07 · source text of arXiv:2112.02187 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. -0.6862(2)
Table II, row 48 x 6, column λ = 8 (2/3-filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.
-0.6855(2), CP-AFQMC (stripe)
Checked 2026-10-07 · source text of arXiv:2112.02187 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. -0.6855(2)
Table II, row 48 x 6, column λ = 12 (filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.
-0.6820(2), CP-AFQMC (stripe)
Checked 2026-10-07 · source text of arXiv:2112.02187 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. -0.6820(2)
Table II, row 48 x 6, column λ = 6 (half-filled stripe state); mixed-estimator constrained-path AFQMC, not a variational bound | Energy per site in units of t, U = 8, hole doping 1/12, 'fully periodic supercells ... with no pinning fields' (Table II caption); 48 x 6 is QMBL's 6 x 48 torus with 132 + 132 electrons.
-0.67820(3), FN-GFMC (Jastrow + BF)
Checked 2026-09-29 · run script scripts/Hubbard/rectangular-6x48_288_P_132_8/FN-stripes/fn_hubbard.sh with datprep.d and datasfn.d, programs/vmc_hubbard/{Prep_stripes_wf.f, Main_stripes_wf.f, Energy.f90, Variance.f} read (varbench/methods@ed31bb0); VarBench history (git clone of github.com/varbench/varbench, partial, read with git log --follow; old names normalised)
Reported as. -195.322 | 0.009 | (VarBench upload by L. F. Tocchio)
48 x 6 torus (the compiled nx = 48, nh = 288; ny = nh/nx = 6), periodic in both directions, t = 1, no t', U = 8 with U n_up n_dn (no constant shift: the diagonal energy is U per doubly occupied site, Main_*_wf.f 'diag(k)=diag(k)-U'), N_up = nelup = 132, N_dn = 288 - neldo = 132 (particle-hole transformed down spins, as the code states for iopt >= 0): the instance. Stripe wavelength 8 as printed. Lattice fixed-node GFMC (gamma = 0) on the VMC state: projected is right; its trial energy etry agrees with the result per site. The M3 flag (FN below the best variational bound) is expected: FN improves on its own trial state. No output log in the repository (scope config). FN not printed in the papers.
-0.67269(3), VMC (Jastrow + BF)
Checked 2026-09-29 · run script scripts/Hubbard/rectangular-6x48_288_P_132_8/VMC-stripes/vmc_hubbard.sh with datprep.d and datasvmc.d, programs/vmc_hubbard/{Prep_stripes_wf.f, Main_stripes_wf.f, Energy.f90, Variance.f} read (varbench/methods@ed31bb0); VarBench history (git clone of github.com/varbench/varbench, partial, read with git log --follow; old names normalised)
Reported as. -193.735 | 0.009 | 19.1 (VarBench upload by L. F. Tocchio)
48 x 6 torus (the compiled nx = 48, nh = 288; ny = nh/nx = 6), periodic in both directions, t = 1, no t', U = 8 with U n_up n_dn (no constant shift: the diagonal energy is U per doubly occupied site, Main_*_wf.f 'diag(k)=diag(k)-U'), N_up = nelup = 132, N_dn = 288 - neldo = 132 (particle-hole transformed down spins, as the code states for iopt >= 0): the instance. Stripe wavelength 8 as printed. Jastrow + backflow VMC: variational is right. The M11 margins over the uniform state are the physics of the stripe state, not an error. No output log in the repository (scope config). Published corroboration: arXiv:1905.02658v2 Table 1, p = 12: '-0.6726(1) (λ = 8)' (size-averaged), stored -0.67269.