Heisenberg triangular, 48 sites

Exact energy and best values (rules §6)

exact	-0.558603	ED Wietek & Läuchli (2018) · the instance is solved

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

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j

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

lattice: triangular
sites: 48
boundary: periodic
energies: 1

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).

Numerically exact (1)

Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established. An exact energy is shown first, before the best of each other class. QMC is exact only within its error bar, which it must state, and reads exact (stochastic); an exact diagonalization outranks it. For a diagonalization resolved by symmetry sector only the ground state's sector is listed; the lowest energies of the other sectors are the instance's spectrum, in its JSON, and are not shown as the exact energy.

E/N (S.S)	distance to class best	σ	Var(E)	V-score	method	source	code	year	comment
-0.558603exact	0	n/a	n/a	n/a	ED peer reviewed	Wietek & Läuchli (2018)		2018

How these numbers were read

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

-0.558603, ED

Checked 2026-10-15 · published PDF Phys. Rev. E 98, 033309 (2018), sources/journal/pre98-033309.pdf, sha256 e8e3383f, pypdf layout; arXiv:1804.05028v2 compared (sources/arxiv/1804.05028v2.pdf, its Table I 'g.s. energy' row identical)

Reported as. -26.812 945 271 5 (S.S total, J = 1); sector Gamma.A1.even

H = J sum S_i . S_j, J = 1 (Eq. 44), energies in units of J ('The energy is given in units of the nearest neighbor coupling constant J = 1'), S.S total; stored Pauli total = 4 x printed. Own ED (Lanczos with sublattice coding). Uploaded to VarBench by the first author (1fa8a1c, A. Wietek, 2022-02-11). sigma null for exact (corrected). peer_reviewed true. 48-site triangular cluster with D6 (file triangular_sqrt48_PP_48).

Coverage

Newest published number here: 2018.

This instance as data

JSON · source file on GitHub · add a result · open an issue about this instance