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Heisenberg triangular 42x42

Record

-0.551429(1) E/N (S.S)

ViT (spatial attention, b = 3, translations + C6v projection)

Viteritti et al. (2026) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑⟨ij⟩ σi·σj

Nearest-neighbour Heisenberg antiferromagnet, J = 1, written with Pauli matrices.

lattice
triangular
sites
1764
boundary
periodic
energies
2

Stored as a total energy in the convention of VarBench; quoted here as E/N (S.S), which is what the papers report (how the conversion works).

Every published energy

Grouped by what the number is. Ranking happens only inside the first group.

Strict variational upper bounds (1)

Where the instance is not solved, the record is the lowest eligible energy in this group; where it is, the lowest eligible energy here is the best variational bound and the closest challenger to the exact one.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.551429record 1.0e-6 n/a n/a ViT (spatial attention, b = 3, translations + C6v projection)
preprint
Viteritti et al. (2026) 2026

Extrapolations (1)

Zero-variance, bond-dimension or Trotter-error extrapolations. Not a bound: no ansatz ever reached the number, so it cannot hold the record.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.55171 1.0e-5 n/a n/a ViT (spatial attention, b = 3, variance → 0)
preprint
Viteritti et al. (2026) 2026

How these numbers were read

Rows added after the VarBench import record where the number came from.

-0.55171(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. -0.55171(1)

Table 1, 42 × 42 block, row 'Zero Variance', printed '-0.55171(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.

-0.551429(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. -0.551429(1)

Table 1, 42 × 42 block, row 'ViT', printed '-0.551429(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.

Coverage

Newest published number here: 2026. 2 rows added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

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