The Hamiltonian
H = ∑⟨ij⟩ σi·σj + J2 ∑⟨⟨ij⟩⟩ σi·σj
J1 = 1, J2 = 0.125, nearest and next-nearest neighbours, written with Pauli matrices.
- lattice
- triangular
- sites
- 108
- boundary
- periodic
- J2
- 0.125
- 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).
How these numbers were read
Rows added after the VarBench import record where the number came from.
-0.5129700 ○ — Thermodynamic-limit estimate interpolated to this size...
Checked 2026-09-14 · arXiv PDF extracted locally with pypdf in layout mode, no LLM transcription
Reported as. -0.51297 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. Column "Exact/Interpolated [10,63]". Per the caption this is NOT an exact energy above 36 sites: it is built from the thermodynamic-limit estimate of Ref. [10] and the exact 36-site energy, assuming finite-size effects scale as 1/L^3. Carried as `extrapolated` (RULES.md 4).
-0.51268(9) — GCNN + Lanczos step
Checked 2026-09-14 · arXiv PDF extracted locally with pypdf in layout mode, no LLM transcription
Reported as. -0.51268 (+/- 0.00009) 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. Column "GCNN+LS" at J2/J1 = 1/8, N = 108. A Lanczos step on a variational state stays variational (RULES.md 4).
-0.51175(7) — GCNN (deep group-equivariant CNN)
Checked 2026-09-14 · arXiv PDF extracted locally with pypdf in layout mode, no LLM transcription
Reported as. -0.51175 (+/- 0.00007) 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 = 1/8, N = 108.
-0.5069(8) — Graph neural network
Checked 2026-09-14 · arXiv PDF extracted locally with pypdf in layout mode, no LLM transcription
Reported as. -0.5069 (+/- 0.0008) 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. Column "Graph NN [64]".