Kitaev (K-J-Γ) honeycomb 6x6 (72 sites), periodic/open, K = 1, J = 0, Gamma = 0

Exact energy and best values (rules §6)

exact	-0.1891314	Exact solution 10.1103/PhysRevB.104.L020409, · 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⟩_γ} [K σ^γ_iσ^γ_j]

Honeycomb lattice; γ = x, y, z labels the three bond directions and (α, β) the other two components. K = 1, J = 0, Γ = 0, the couplings of the spin-1/2 form with S = σ/2, normalised to |K| = 1 (RULES.md 2.1); written here with Pauli matrices, so the stored energy is 4 times the S-operator energy and E/N in S units is E/(4N).

lattice: honeycomb-6x6
sites: 72
boundary: periodic/open
K: 1
J: 0
Gamma: 0
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
-0.1891314exact	0	n/a	n/a	n/a	Exact solution peer reviewed	10.1103/PhysRevB.104.L020409,		2021

How these numbers were read

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

-0.1891314, Exact solution

Checked 2026-10-20 · source text of arXiv:2009.04129 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-20)

Reported as. -54.469847490329

Supplemental Material, numerical data for Fig. 3: Eg(Phi_y = 1) of the 6 x 6 cylinder; the Phi_y = -1 sector is higher (-54.385529432483, 'about 0.084' above, main text); version read: arXiv text (sources/2009.04129.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Eq. (1) H3 = sum J_a sigma^a sigma^a + J3 sum sigma^x sigma^y sigma^z, Pauli matrices, J_a = 1, J3 = 0: K = +4 in the S = sigma/2 form, 4 times the instance's K = +1 (scale 4). Total energy of the 72-site cylinder (Supplemental Material, numerical data for Fig. 3); the boundary term of Eq. (S8) has deltaK -> 0+ and commutes with H3. QMBL's flux-free free-Majorana energy of the 6 x 6 cylinder gives -54.4698475.

Coverage

Newest published number here: 2021.

This instance as data

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