Heisenberg rectangular 24x48, periodic/open

Exact energy and best values (rules §6)

exact (stochastic)	-0.6651098(6)	SSE QMC Sandvik (2026) · sign-problem-free QMC, exact within its error bar

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: rectangular-24x48
sites: 1152
boundary: periodic/open
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
-0.6651098exact (stochastic)	0	5.9e-7	n/a	n/a	SSE QMC peer reviewed	Sandvik (2026)		2026

How these numbers were read

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

-0.6651098(6), SSE QMC

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

Reported as. E0/N_b = 0.3360555(3) (magnitude, per bond, N_b = 4L^2 - L = 2280; the caption prints 2L^2 - L), L x 2L = 24 x 48, 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 = 24. The caption's N_b is a misprint: the cylinder has 4L^2 - L = 2280 bonds, and only that count sends E0/N_b to the infinite-size value the Fig. 8 fits share with Tables 1 and 2. Boundary PO (VarBench lattice.md): periodic along the 24-site direction, open along the 48-site one. Printed as a magnitude; E/N = -(E0/N_b) N_b / N = -0.66510984 in S.S units, Pauli total = 4 N E/N.

Coverage

Newest published number here: 2026.

This instance as data

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