How these numbers were read
Where each number below was read, and how it was checked.
-0.42987(1), VMC (Gutzwiller)
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. | -330.143 | 0.011 | 42.3 | 192 | 0 | VMC with Dirac spin liquid + Jastrow | [code](https://github.com/varbench/methods/blob/main/scripts/Heisenberg/kagome-8x8_192_P/vmc_gutzwiller.sh) |
Record (no exact row). vmc_gutzwiller inputs: 6-site supercell x '4 0 0 8' = 8x8 kagome cells = 192 sites, periodic spin torus (abs(ivicn); '1 0' = antiperiodic auxiliary fermions along a1), nelup = neldo = 96 (Sz = 0), jperp = 1, uvv = 0.25 (H = J sum S.S, no constant), Dirac spin liquid ([0,pi] fluxes) + spin Jastrow (iesspin=27), VMC measurement (itestr=2, ngen = 5e5), read_ene.x binned error (bins of 10^4, first 4 dropped). Stored = 4N x <H>/N: -0.4298737 per site (S.S). The instance's other rows are projected Dirac spin liquids without Jastrow (He, Yu & Li -0.42868(3) P-A, -0.42724(3) P-P; Ran et al. -0.42866): the Jastrow lowers the energy by 1.2e-3 per site, which is the M11 0.28% margin. V-score 0.0745, the same as the 48-site row of the same code (0.0745): one wave-function class. sigma/sqrt(Var/2^20) = 1.73 (binned; implied 3.5e5 effective samples). No independent value: config only. Entered d940e97 (2022-02-14, F. Ferrari), never changed; linked by Ferrari d186176 (2024-07-30). Not published in the dataset paper (arXiv:2302.04919 prints no energies).
-0.42868(3), VMC (Gutzwiller)
Checked 2026-09-15 · source text of arXiv:2407.20629 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; verified 2026-09-16 by an independent second reading (arXiv versions, VarBench history)
Reported as. 0.42868 ± 0.00003 (printed without a sign)
Supplemental Material S4 of arXiv:2407.20629 (identical in the PRL supplement) | 8x8x3 = 192-site periodic kagome torus, H = J sum S_i.S_j (Eq. 1), energy per site | Printed unsigned ("E = 0.42868 ± 0.00003 (E = 0.42724 ± 0.00003) for P-A (periodic-periodic (P-P)) BC"); the sign is the paper's own: its Fig. S7 plots the same quantity on an axis from -0.4280 to -0.4290, and it quotes Ran et al.'s -0.42866(2) as 0.42866(2). P-A and P-P are boundary conditions on the spinon mean-field state; the spin torus is periodic in both, as in VarBench's own baseline for this cluster. The paper does not say how the degenerate Dirac-point level is filled under P-P.
-0.42866(2), VMC (Gutzwiller)
Checked 2026-09-15 · source text of arXiv:cond-mat/0611414 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; located by the independent verification of arXiv:2407.20629, which quotes it
Reported as. -0.42866(2)
Table I of arXiv:cond-mat/0611414 (SL-[0,pi], 8x8x3 lattice), text committed as sources/cond-mat-0611414.txt | energy per site in units of J (caption); "mixed boundary conditions; i.e., periodic along one Bravais lattice vector, and anti-periodic" applies to the spinon mean-field state, the spin torus is periodic
-0.42724(3), VMC (Gutzwiller)
Checked 2026-09-15 · source text of arXiv:2407.20629 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; verified 2026-09-16 by an independent second reading (arXiv versions, VarBench history)
Reported as. 0.42724 ± 0.00003 (printed without a sign)
Supplemental Material S4 of arXiv:2407.20629 (identical in the PRL supplement) | 8x8x3 = 192-site periodic kagome torus, H = J sum S_i.S_j (Eq. 1), energy per site | Printed unsigned ("E = 0.42868 ± 0.00003 (E = 0.42724 ± 0.00003) for P-A (periodic-periodic (P-P)) BC"); the sign is the paper's own: its Fig. S7 plots the same quantity on an axis from -0.4280 to -0.4290, and it quotes Ran et al.'s -0.42866(2) as 0.42866(2). P-A and P-P are boundary conditions on the spinon mean-field state; the spin torus is periodic in both, as in VarBench's own baseline for this cluster. The paper does not say how the degenerate Dirac-point level is filled under P-P.