Heisenberg shuriken, 24 sites

Exact energy and best values (rules §6)

exact	-0.4483291	ED Astrakhantsev et al. (2021) · 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: shuriken
sites: 24
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
-0.4483291exact	0	n/a	0.00e+0	0.0e+0	ED	Astrakhantsev et al. (2021)		2021

How these numbers were read

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

-0.4483291, ED

Checked 2026-10-15 · published PDF Phys. Rev. B 104, L220408 (2021), sources/journal/prb104-L220408.pdf, sha256 3743eedf, and the APS Supplemental Material (Shuriken_SupplementalMaterial.pdf, sources/journal/prb104-L220408-supp.pdf, sha256 cf37498d), pypdf plain + layout; arXiv:2110.08198v3 compared via the 2026-09-29/30 pass

Reported as. plotted point only ('ED', blue star at 24 sites); no printed digits in the journal main text or SM (searched for 'exact', 'Lanczos', 0.44...)

Journal caption and SM unchanged against arXiv v3: 24-site D4-symmetric 6 x 2^2 shuriken cluster, J_square = J_triangle = J (SM Fig. S1: 'Our study focuses on ... J_square = J_triangle = J'), periodic. The value rests on QMBL's two-code recomputation, not on a printed number; reference to the paper (which shows the ED point) and peer review (Editors' Suggestion, published 22 December 2021) stand. sigma 0 / variance 0 for an exact row are VarBench placeholders (sigma would read null elsewhere in the table; loader-level). No duplicate.

Coverage

Newest published number here: 2021. Literature last checked 2026-09-15 (citation screen of Astrakhantsev et al. 2021 (PRB 104, L220408, shuriken): citing works from OpenAlex and Semantic Scholar (scripts/cited_by.mjs)): 8 papers read, 0 of them with an energy on this page.

This instance as data

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