Heisenberg rectangular 18x36, periodic/open

Heisenberg/rectangular-18x36_648_PO

No record

—

solved exactly (rules §6). Every row is still listed below.

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j

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

lattice: rectangular-18x36
sites: 648
boundary: periodic/open
energies: 1

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.

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
-0.3272005(2)	1.9e-7	n/a	n/a	SSE QMC (stochastic series expansion), T -> 0 converged at beta/L = 32 and 64 preprint	Sandvik (2026)	2026

How these numbers were read

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

-0.3272005(2) — SSE QMC (stochastic series expansion), T -> 0 converged at...

Checked 2026-09-15 · arXiv HTML parsed locally, one value per table cell; no LLM transcription

Reported as. E0/N_b = 0.3365491(2) (magnitude, per bond, N_b = 630), L x 2L = 18 x 36, cylinder

Table 3, "SSE data for L x 2L lattices with cylindrical boundary conditions (periodic in the shorter direction and open in the longer direction). The ground state energy is normalized by the number of interaction bonds N_b = 2 L^2 - L", row L = 18. Boundary PO (VarBench lattice.md): periodic along the 18-site direction, open along the 36-site one. Printed as a magnitude; E/N = -(E0/N_b) N_b / N = -0.32720051 in S.S units, Pauli total = 4 N E/N.

Coverage

Newest published number here: 2026. 1 row added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

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