J1-J2 square, 40 sites, J2 = 0.5

J1J2/square_40_P_0.5

No record

—

solved exactly (rules §6). Every row is still listed below.

The Hamiltonian

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

J₁ = 1, J₂ = 0.5, nearest and next-nearest neighbours, written with Pauli matrices.

lattice: square
sites: 40
boundary: periodic
J2: 0.5
energies: 1

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.

Numerically exact (1)

Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established: the answer, not a claim about it.

E/N (S.S)	σ	Var(E)	V-score	method	source	year
-0.4990762	n/a	n/a	n/a	Exact diagonalization (Lanczos) peer reviewed	Richter & Schulenburg, The spin-	n/a

How these numbers were read

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

-0.4990762 — Exact diagonalization (Lanczos)

Checked 2026-09-15 · arXiv PDF extracted locally with pypdf in layout mode, parsed by column position and checked against the paper's own per-site column; no LLM transcription

Reported as. E_GS(S = 0) = -19.96304839 (total, S.S, J1 = 1), N = 40, J2 = 0.5

Table 1, "Ground state energy E_GS(S = 0) ...", row J2 = 0.5. The tilted 40-site square-lattice cluster of the paper's Fig. 1 with periodic boundaries (Sec. 2); E/N = -0.4990762 in S.S units, Pauli total = 4 E. The paper's J2 grid is 0, 0.1, ..., 0.5, 0.55, 0.6, 0.65, 0.7, 0.8, 0.9, 1.0.

Coverage

No row here carries a publication year. 1 row 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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