J1-J2 square 6x6, J2 = 0.65

Record

-0.5065880 E/N (S.S)

Schulz et al. (1996) · exact energy: the instance is solved, and this is the state of the art on it (rules §6)

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j + J₂ ∑_{⟨⟨ij⟩⟩} σ_i·σ_j

J₁ = 1, J₂ = 0.65, nearest and next-nearest neighbours, written with Pauli matrices.

lattice: square
sites: 36
boundary: periodic
J2: 0.65
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)	σ	Var(E)	V-score	method	source	year
-0.5062990	n/a	n/a	n/a	ViT preprint ineligible: sampled, no error bar	Golubev et al. (2026)	2026

Numerically exact (1)

Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established: the answer, not a claim about it, and therefore the record wherever one exists. QMC is exact only within its statistical error bar, which it must state, and its rows read exact (stochastic); an exact diagonalization outranks it. Sector-resolved diagonalizations state the lowest energy in one symmetry sector and do not hold it.

E/N (S.S)	σ	Var(E)	V-score	method	source	year
-0.5065880record	n/a	n/a	n/a	ED peer reviewed	Schulz et al. (1996)	1996

How these numbers were read

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

-0.5065880 — ED

Checked 2026-09-28 · source text of arXiv:cond-mat/9402061 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. -0.506588

Table II, row J2 = 0.65, column 36(A1) (36(B1) -0.506582 is higher). QMBL's Lanczos (qmbl-runs/qmbl-ed-2026-09-28: E2's ed_sym.py, C4v one-dimensional sectors with even spin at k = 0 and M) gives -0.506587859 per site, so the printed value is the correctly rounded ground-state energy. Golubev et al. (arXiv:2606.04558 Table I, 6x6 ED) print -0.506590, 2.1e-6 below it | Ground-state energy per site, J1 = 1, S.S units; the same column reproduces QMBL's exact 36-site rows at J2 = 0, 0.3, 0.4, 0.5, 0.6 to 1e-6.

-0.5062990 — ViT

Checked 2026-09-28 · source text of arXiv:2606.04558 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. -0.506299

Table I, row J2=0.65, column '6×6, ViT (this work)' | Table I prints energy per site in S.S units: its J2 = 0 QMC column equals Sandvik's exact values on Heisenberg/square_64_P and square_100_P.

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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