Heisenberg triangular, 108 sites

Heisenberg/triangular_108_P

Record

-0.55315(3) E/N (S.S)

GCNN (deep group-equivariant CNN)

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: 108
boundary: periodic
energies: 2

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
-0.55315(3)record	3.0e-5	n/a	n/a	GCNN (deep group-equivariant CNN) peer reviewed	Roth et al. (2022)	2022
-0.5519(4)	4.0e-4	n/a	n/a	Graph neural network quoted from another paper	Kochkov et al. (2021)	2021

How these numbers were read

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

-0.55315(3) — GCNN (deep group-equivariant CNN)

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

Reported as. -0.55315 (+/- 0.00003) per site in S.S units

Read from Table III of arXiv:2211.07749 (J1-J2 triangular lattice, periodic, energies in units of J1 per spin, i.e. the S.S per-site convention), extracted from the PDF with pypdf in layout mode so the column positions are unambiguous. Row J2/J1 = 0, N = 108.

-0.5519(4) — Graph neural network

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

Reported as. -0.5519 (+/- 0.0004) per site in S.S units

Coverage

Newest published number here: 2022. 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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