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All instances / Heisenberg

Heisenberg square 16x16, open

Heisenberg/square_256_O

Record

-0.643504(3) E/N (S.S)

2D minGRU (3 layers, c4v symmetry, parallel scan)

Merali et al. (2026) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑⟨ij⟩ σi·σj

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

lattice
square
sites
256
boundary
open
energies
4

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.

Strict variational upper bounds (3)

The record is the lowest eligible energy in this group, and only this group.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.643504(3)record 3.0e-6 n/a n/a 2D minGRU (3 layers, c4v symmetry, parallel scan)
preprint
Merali et al. (2026) 2026
-0.643448(1) 1.0e-6 n/a n/a PixelCNN (deep autoregressive)
quoted from another paper
Sharir, Levine, Wies, Carleo & S n/a
-0.643391(3) 3.0e-6 n/a n/a Finite PEPS, gradient optimization
quoted from another paper
Liu, Dong, Han, Guo & He, Gradie n/a

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)σVar(E)V-score methodsourceyear
-0.6435317(2) 2.0e-7 n/a n/a QMC (stochastic series expansion)
quoted from another paper
Sandvik (2026) 2026

How these numbers were read

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

-0.6435317(2) — QMC (stochastic series expansion)

Checked 2026-09-14 · arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription

Reported as. -0.6435317 (+/- 2e-7) per site in S.S units

Read from Table 2 of arXiv:2605.13807 (2D Heisenberg, square lattice, OBC, E/N in S.S units), parsed from the arXiv HTML. Column "QMC [49]" = arXiv:2601.20189.

-0.643504(3) — 2D minGRU (3 layers, c4v symmetry, parallel scan)

Checked 2026-09-14 · arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription

Reported as. -0.643504 (+/- 0.000003) per site in S.S units

Read from Table 2 of arXiv:2605.13807 (2D Heisenberg, square lattice, OBC, E/N in S.S units), parsed from the arXiv HTML. The citing paper's own result; 29 GPU-days on a single L40S.

-0.643448(1) — PixelCNN (deep autoregressive)

Checked 2026-09-14 · arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription

Reported as. -0.643448 (+/- 0.000001) per site in S.S units

Read from Table 2 of arXiv:2605.13807 (2D Heisenberg, square lattice, OBC, E/N in S.S units), parsed from the arXiv HTML. Column "PixelCNN [52]".

-0.643391(3) — Finite PEPS, gradient optimization

Checked 2026-09-14 · arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription

Reported as. -0.643391 (+/- 0.000003) per site in S.S units

Read from Table 2 of arXiv:2605.13807 (2D Heisenberg, square lattice, OBC, E/N in S.S units), parsed from the arXiv HTML. Column "PEPS [33]".

Coverage

Newest published number here: 2026. 4 rows 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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