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All instances / Heisenberg

Heisenberg triangular, 108 sites

Best values (rules §6)

best variational -0.55315(3) VMC (GCNN)
Roth et al. (2022) · the lowest unflagged variational energy, a strict variational bound

Energies as E/N (S.S). Classes are different claims and are not ranked against each other.

The Hamiltonian

H = ∑⟨ij⟩ σi·σj

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

lattice
triangular
sites
108
boundary
periodic
energies
2

Stored as a total energy; 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. The exact energy comes first where there is one; in every other group the lowest unflagged energy is its best value, and each row's distance is to that best (rules §6).

Strict variational upper bounds (2)

Energies that a variational state reached (VMC, DMRG and MPS at finite bond dimension, PEPS, NQS, VQE). Each is an upper bound on the ground-state energy.

E/N (S.S)distance to class bestσVar(E)V-score methodsourcecodeyearcomment
-0.55315best variational 0 3.0e-5 n/a n/a VMC (GCNN)
peer reviewed
 Roth et al. (2022) uses NetKet 2022
-0.5519 1.2e-3 4.0e-4 n/a n/a VMC (GNN)
preprint
 Kochkov et al. (2021) 2021

How these numbers were read

Where each number below was read, and how it was checked.

-0.55315(3), VMC (GCNN)

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), VMC (GNN)

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

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]" at J2/J1 = 0, N = 108 = arXiv:2110.06390.

Coverage

Newest published number here: 2022. Literature last checked 2026-09-15 (table harvest of cached arXiv sources (match_tables.mjs --all), every matched paper read for this instance): 1 paper read, 0 of them with an energy on this page.

This instance as data

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