Heisenberg square 60x60

Exact energy and best values (rules §6)

exact (stochastic)	-0.66945260(3)	SSE QMC Sandvik (2026) · sign-problem-free QMC, exact within its error bar

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: 3600
boundary: periodic
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
-0.66945260exact (stochastic)	0	3.0e-8	n/a	n/a	SSE QMC peer reviewed	Sandvik (2026)		2026

How these numbers were read

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

-0.66945260(3), SSE QMC

Checked 2026-09-15 · arXiv HTML parsed locally, one value per table cell; no LLM transcription

Reported as. e0 = -0.66945260(3) per spin (S.S), L = 60, periodic

Table 1, "Results for different system sizes computed at inverse temperature beta/L = 64 for L > 30 and averaged over beta/L = 32 and beta/L = 64 simulations for L <= 30", column e0, row L = 60. Pauli total = 4 N e0. The L = 6 value agrees with the exact-diagonalization row on square_36_P to 1.6e-8.

Coverage

Newest published number here: 2026.

This instance as data

JSON · source file on GitHub · add a result · open an issue about this instance