Heisenberg kagome 4x4 (48 sites)

Heisenberg/kagome-4x4_48_P

Record

-0.4375(2) E/N (S.S)

GCNN (6 layers, 6 feature maps), symmetric ansatz

Đurić et al. (2024) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j

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

lattice: kagome-4x4
sites: 48
boundary: periodic
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 (2)

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

E/N (S.S)	σ	Var(E)	V-score	method	source	year
-0.4375(2)record	2.1e-4	n/a	n/a	GCNN (6 layers, 6 feature maps), symmetric ansatz peer reviewed	Đurić et al. (2024)	2024
-0.43043(3)	2.6e-5	1.06e+1	7.4e-2	VMC with Dirac spin liquid + Jastrow VarBench reference run	run script, no paper cited	n/a

Extrapolations (1)

Zero-variance, bond-dimension or Trotter-error extrapolations. Not a bound: no ansatz ever reached the number, so it cannot hold the record.

E/N (S.S)	σ	Var(E)	V-score	method	source	year
-0.4383(2)	2.0e-4	n/a	n/a	DMRG, truncation-error extrapolated (Torus 4) peer reviewed	Depenbrock et al. (2012)	2012

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)	σ	Var(E)	V-score	method	source	year
-0.438703897156(2)	2.1e-12	n/a	n/a	Exact Diagonalization	Wietek & Läuchli (2018)	2018

How these numbers were read

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

-0.4383(2) — DMRG, truncation-error extrapolated (Torus 4)

Checked 2026-09-14 · arXiv PDF text extracted locally with pypdf, no LLM transcription

Reported as. -0.4383 per site in S.S units

Table I row "Torus 4 -0.4383(2)". The paper states energies are "extrapolated in the truncation error of single-site DMRG", so this is not a strict variational bound (RULES.md 4). Sits above the exact -0.4387039 on this instance.

-0.4375(2) — GCNN (6 layers, 6 feature maps), symmetric ansatz

Checked 2026-09-14 · arXiv PDF text extracted locally with pypdf, no LLM transcription

Reported as. -0.4375 per site in S.S units

Sec. III: "R = (E_GCNN - E_ED)/E_ED ~ 0.3% with E_ED = -21.057787063 and E_GCNN = -21.00 +/- 0.01" on the 48-site (4x4x3) PBC cluster, chi0 sector. Total energy in S.S units; E/N = -0.4375. The instance's existing exact row is -0.4387039, i.e. -21.057787063/48 to 8 digits, which confirms the cluster and the convention. Sampling here is the ergodic spin-exchange update, so the objection in arXiv:2605.28861 does not apply to this size.

Coverage

Newest published number here: 2024. 2 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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