J1-J2 square, 40 sites, J2 = 1

Exact energy and best values (rules §6)

exact	-0.7109702	ED Richter & Schulenburg (2009) · the instance is solved

Energies as E/N (S.S). Classes are different claims and are not ranked against each other.

The Hamiltonian

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

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

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

Stored as a total energy; 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. The exact energy comes first where there is one; in every other group the lowest unflagged energy is its best value, and each row's distance is to that best (rules §6).

Numerically exact (1)

Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established. An exact energy is shown first, before the best of each other class. QMC is exact only within its error bar, which it must state, and reads exact (stochastic); an exact diagonalization outranks it. For a diagonalization resolved by symmetry sector only the ground state's sector is listed; the lowest energies of the other sectors are the instance's spectrum, in its JSON, and are not shown as the exact energy.

E/N (S.S)	distance to class best	σ	Var(E)	V-score	method	source	code	year	comment
-0.7109702exact	0	n/a	n/a	n/a	ED peer reviewed	Richter & Schulenburg (2009)		2009

How these numbers were read

Where each number below was read, and how it was checked.

-0.7109702, ED

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) = -28.43880892 (total, S.S, J1 = 1), N = 40, J2 = 1

Table 1, "Ground state energy E_GS(S = 0) ...", row J2 = 1. The tilted 40-site square-lattice cluster of the paper's Fig. 1 with periodic boundaries (Sec. 2); E/N = -0.7109702 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

Newest published number here: 2009.

This instance as data

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