Heisenberg square 52x52, open

Best values (rules §6)

best variational	-0.660967(4)	VMC (minGRU) Merali et al. (2026) · the lowest unflagged variational energy, a strict variational bound

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: 2704
boundary: open
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).

Strict variational upper bounds (1)

Energies that a variational state reached (VMC, DMRG and MPS at finite bond dimension, PEPS, NQS, VQE). Each is an upper bound on the ground-state energy.

E/N (S.S)	distance to class best	σ	Var(E)	V-score	method	source	code	year	comment
-0.660967best variational	0	4.0e-6	n/a	n/a	VMC (minGRU) preprint	Merali et al. (2026)		2026

How these numbers were read

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

-0.660967(4), VMC (minGRU)

Checked 2026-10-27 · arXiv:2605.13807: arXiv:2605.13807v1 (only version; no journal reference on 2026-10-27): pypdf layout text sources/2605.13807.txt read locally, checked against Table 6 of the arXiv HTML sources/2605.13807.html; no LLM transcription; single reading

Reported as. -0.660967(4)

TABLE VI, row N = 52^2 (line 702 of sources/2605.13807.txt) | energy per site in S.S units, J = 1, open boundaries (caption: '2D Heisenberg model with OBC'); same convention as the table's QMC column, which equals the stored SSE rows at every size it covers; the table prints no QMC value at this size

Coverage

Newest published number here: 2026.

This instance as data

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