Record
-0.551602(1)
E/N (S.S)
ViT (spatial attention, b = 3, translations + C6v projection)
Viteritti et al. (2026) · lowest eligible strict variational bound
(rules §6)
How these numbers were read
Rows added after the VarBench import record where the number came from.
-0.55189(1) — ViT (spatial attention, b = 3, variance → 0)
Checked 2026-09-28 · source text of arXiv:2602.02665 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading, parsed from the committed HTML table and matched against the PDF text
Reported as. -0.55189(1)
Table 1, 24 × 24 block, row 'Zero Variance', printed '-0.55189(1)', 'This work'; caption: 'For each system size the zero-variance extrapolated energy is also reported'. Sec. V.3 / Fig. 6: linear fit of energy against variance per site over the unprojected, translation-projected and fully projected ViT states at this L; an extrapolation of the same runs, not a separate calculation. | Table 1 prints ground-state energies per site of the spin-1/2 triangular Heisenberg model on periodic L x L clusters (Sec. III: 'All calculations are performed on periodic L x L clusters with L chosen as a multiple of 3', H = J sum S_i.S_j), S.S units. Magnitude check: the values lie between -0.5517 and -0.5520, next to the 12 x 12 value -0.55315 (GCNN, per site, S.S) on Heisenberg/triangular_144_P, not four times it (Pauli) or a total.
-0.551602(1) — ViT (spatial attention, b = 3, translations + C6v...
Checked 2026-09-28 · source text of arXiv:2602.02665 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading, parsed from the committed HTML table and matched against the PDF text
Reported as. -0.551602(1)
Table 1, 24 × 24 block, row 'ViT', printed '-0.551602(1)', 'This work'; caption: 'The results of this work are obtained by enforcing translational and C6v point-group symmetries (refer to Section V.2)'. | Table 1 prints ground-state energies per site of the spin-1/2 triangular Heisenberg model on periodic L x L clusters (Sec. III: 'All calculations are performed on periodic L x L clusters with L chosen as a multiple of 3', H = J sum S_i.S_j), S.S units. Magnitude check: the values lie between -0.5517 and -0.5520, next to the 12 x 12 value -0.55315 (GCNN, per site, S.S) on Heisenberg/triangular_144_P, not four times it (Pauli) or a total.
-0.54810(6) — 2D RNN (iterative retraining, s = 4.0, r = 0.158)
Checked 2026-09-28 · authors' data release read locally (pickle via numpy), values copied by key, no transcription; the file is committed as sources/2505.20406-repo-final_energies_data.json and reproduces Table V's L = 6 energy and Table II's V-scores
Reported as. -0.5481048689948188 +/- 0.00005594673281008129 per site (S.S), Var(E/N) = 0.00003130036912122626, V-score 0.06001290121315589
github.com/mschuylermoss/HeisenbergRNN, commit 5f5cffa5cb (2025-10-28, HEAD; file last changed in d58a945cd4 2025-05-27, 'final plotting data and plotting notebooks'), Triangular/final_plotting/plotting_data/final_energies_data_plotting.pkl, sha256 bdc59e5bc3780fb4ea7444400dc9abd9984a6a259ab03f9299c1f80edb87d276: ['TriangularMS,periodicBC']['scale=4.0,rate=0.158,T=1.00'], L = 24. The paper's most accurate schedule (Table II, whose L = 24 V-score 6.0e-2 is this run's 0.0600); plotted in Fig. 4(a), not printed; quoted as -0.54810(1) in Table 1 of arXiv:2602.02665, whose error bar is not the primary's. TriangularMS is the 120-degree basis rotation U_tri, which changes the representation, not the Hamiltonian. Variance is Var(H)/N^2 in S.S units; total = var x N^2 x 16.