Heisenberg triangular 6x6

Heisenberg/triangular_36_P

Record

-0.560313(3) E/N (S.S)

Group CNN (deep, symmetry-projected)

Roth et al. (2022) · 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: triangular
sites: 36
boundary: periodic
energies: 8

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 (7)

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
-0.560313(3)record	3.0e-6	n/a	n/a	Group CNN (deep, symmetry-projected)	Roth et al. (2022)	2022
-0.5601(4)	4.0e-4	n/a	n/a	Lattice Convolutional Network	Fu et al. (2022)	2022
-0.5592200 ○	n/a	n/a	n/a	Group CNN ineligible: sampled, no error bar	Roth & MacDonald (2021)	2021
-0.5581022	n/a	7.07e+0	3.9e-2	DMRG (bond dimension = 2048) VarBench reference run	run script, no paper cited	n/a
-0.5562(2)	2.0e-4	n/a	n/a	2D RNN wavefunction (iterative retraining, s=4.0, r=0.158) preprint	Moss et al. (2025)	2025
-0.49161(5)	4.5e-5	4.35e+1	3.1e-1	RBM (alpha = 1) VarBench reference run	run script, no paper cited	n/a
-0.48678(4)	4.2e-5	3.70e+1	2.7e-1	Jastrow baseline VarBench reference run	run script, no paper cited	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)	σ	Var(E)	V-score	method	source	year
-0.5603734	n/a	n/a	n/a	Exact diagonalization VarBench reference run	run script, no paper cited	n/a

How these numbers were read

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

-0.560313(3) — Group CNN (deep, symmetry-projected)

Checked 2026-09-14 · found in the citing paper's comparison table, then confirmed in the primary source's own PDF (pypdf); no LLM transcription

Reported as. -0.560313 (+/- 0.000003) per site in S.S units

Read from Table 5 of arXiv:2505.20406 (TLAHM, L=6 triangular lattice, PBC, E/N in S.S units), parsed from the arXiv HTML. Row "Group Convolutional Neural Network [32]" = arXiv:2211.07749. Sits 6.0e-5 ABOVE the exact -0.5603734 already on this instance, as a variational bound must. CONFIRMED IN PRIMARY SOURCE - arXiv:2211.07749, results table: "J2/J1 N GCNN ... Exact/Interpolated ... 0 36 -0.560313(3) - -0.5603734" - the GCNN energy at J2/J1 = 0, N = 36, printed beside the exact value.

-0.5601(4) — Lattice Convolutional Network

Checked 2026-09-14 · found in the citing paper's comparison table, then confirmed in the primary source's own PDF (pypdf); no LLM transcription

Reported as. -0.5601 (+/- 0.0004) per site in S.S units

Read from Table 5 of arXiv:2505.20406 (TLAHM, L=6 triangular lattice, PBC, E/N in S.S units), parsed from the arXiv HTML. Row "Lattice Convolutional Network [49]" = arXiv:2206.07370. CONFIRMED IN PRIMARY SOURCE - arXiv:2206.07370, results table: "Triangular 36 0 - -0.55889 -0.5601(4) -0.5603734" - the special-kernel LCN energy at J2 = 0 on the 36-site triangular lattice.

-0.5592200 ○ — Group CNN

Checked 2026-09-14 · found in the citing paper's comparison table, then confirmed in the primary source's own PDF (pypdf); no LLM transcription

Reported as. -0.55922 per site in S.S units

Read from Table 5 of arXiv:2505.20406 (TLAHM, L=6 triangular lattice, PBC, E/N in S.S units), parsed from the arXiv HTML. Row "Group Convolutional Neural Network [104]" = arXiv:2104.05085. No error bar is given in the table, so under RULES.md 6 this sampled row cannot hold a record. CONFIRMED IN PRIMARY SOURCE - arXiv:2104.05085, results table: "J2 = 0 ... ED [28] -0.5603734 ... G-CNN -0.55922".

-0.5562(2) — 2D RNN wavefunction (iterative retraining, s=4.0, r=0.158)

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

Reported as. -0.5562 (+/- 0.0002) per site in S.S units

Read from Table 5 of arXiv:2505.20406 (TLAHM, L=6 triangular lattice, PBC, E/N in S.S units), parsed from the arXiv HTML. The citing paper's own result.

Coverage

Newest published number here: 2025. 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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