Heisenberg square, 40 sites

Exact energy and best values (rules §6)

exact	-0.6773713	ED Richter et al. (2004) · 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

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

lattice: square
sites: 40
boundary: periodic
energies: 2

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 (2)

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
-0.6773713	0	n/a	n/a	n/a	ED peer reviewed	Richter & Schulenburg (2009)		2009
-0.6773713exact	0	n/a	n/a	n/a	ED book chapter	Richter et al. (2004)		2004

How these numbers were read

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

-0.6773713, 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) = -27.09485025 (total, S.S, J1 = 1), N = 40, J2 = 0

Table 1, "Ground state energy E_GS(S = 0) ...", row J2 = 0. The tilted 40-site square-lattice cluster of the paper's Fig. 1 with periodic boundaries (Sec. 2); E/N = -0.6773713 in S.S units, Pauli total = 4 E. J2 = 0 is the plain Heisenberg antiferromagnet on this cluster.

-0.6773713, ED

Checked 2026-10-24 · arXiv:cond-mat/0412662: publisher PDF (Springer, scanned) Table 2.1, read from the page image rendered at 200 %; checked against the arXiv text (pypdf layout and plain modes); no LLM transcription of numbers; single reading + page-image check

Reported as. −27.0948503

Table 2.1 (p. 102), row N = 40, edge vectors (2, 6), (-6, 2), column E0. The mirror image of the cluster of Richter & Schulenburg, EPJB 73, 117 (2010), T1 = (6, 2), T2 = (-2, 6); a reflection of the square lattice maps one onto the other, so the spectra agree. That paper prints -27.09485025, this value to one more digit. | Spin-1/2 Heisenberg antiferromagnet H = J sum_<ij> S_i . S_j on the square lattice, J = 1, periodic boundaries on the finite lattice defined by the two edge vectors printed in the row (Betts construction, Sec. 2.4.1); E0 is the total singlet ground-state energy in S.S units, stored as the Pauli total 4 E0. Version read: publisher PDF (Springer, a scan), Table 2.1 on p. 102 read from the page image; identical to Table 1 of the arXiv text cond-mat/0412662. Peer review: a chapter of an edited lecture-notes volume, not a refereed journal.

Coverage

Newest published number here: 2009.

This instance as data

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