The Hamiltonian
H = ∑⟨ij⟩γ [K σγiσγj]
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-4x4
- sites
- 32
- boundary
- periodic
- K
- -1
- J
- 0
- Gamma
- 0
- energies
- 5
Stored as a total energy; quoted here as
E/N (S.S), which is what the papers report
(how the conversion works).
How these numbers were read
Where each number below was read, and how it was checked.
-0.1963139, ED
Checked 2026-10-20 · source text of arXiv:1411.5198 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. −12.56409
Table I, row Exact, column 4×4 unit cells; version read: arXiv text (sources/1411.5198.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Eq. (28) H_KH = 2 alpha H_K + (1 - alpha) J_H sum S.S at alpha = 1 (the text before Table I: 'the Kitaev model, where alpha = 1'), with H_K = -J sum S^g S^g (Eq. 27), S^g = c^dag sigma^g c / 2, J = 1: H = -2 sum S^g S^g, K = -2 in the S = sigma/2 form, twice the instance's K = -1 (scale 2). Total energies of the cluster: the per-site values -0.3970, -0.3977, -0.3926 the text compares with the thermodynamic -0.39365 are these totals over N. QMBL's flux-free free-Majorana energies of the 3 x 4 and 4 x 4 tori reproduce -9.54589 and -12.56409 (SWEEP.md, 2026-10-20).
-0.19617(8), VMC (PP)
Checked 2026-10-20 · source text of arXiv:1411.5198 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. −12.555 ± 0.005
Table I, row |ψKL⟩, column 4×4 unit cells; version read: arXiv text (sources/1411.5198.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Eq. (28) H_KH = 2 alpha H_K + (1 - alpha) J_H sum S.S at alpha = 1 (the text before Table I: 'the Kitaev model, where alpha = 1'), with H_K = -J sum S^g S^g (Eq. 27), S^g = c^dag sigma^g c / 2, J = 1: H = -2 sum S^g S^g, K = -2 in the S = sigma/2 form, twice the instance's K = -1 (scale 2). Total energies of the cluster: the per-site values -0.3970, -0.3977, -0.3926 the text compares with the thermodynamic -0.39365 are these totals over N. QMBL's flux-free free-Majorana energies of the 3 x 4 and 4 x 4 tori reproduce -9.54589 and -12.56409 (SWEEP.md, 2026-10-20).
-0.1961(2), VMC (PP)
Checked 2026-10-20 · source text of arXiv:1411.5198 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. −12.55±0.01
Table II, 4×4 unit cells, (Wx,Wy) = (+,+), column VMC; version read: arXiv text (sources/1411.5198.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8); The text names the three degenerate 4 x 4 sectors (1,-1), (-1,1), (-1,-1); Table II lists (+,+), (+,-), (-,+). The sector label is copied from the table. | Eq. (28) H_KH = 2 alpha H_K + (1 - alpha) J_H sum S.S at alpha = 1 (the text before Table I: 'the Kitaev model, where alpha = 1'), with H_K = -J sum S^g S^g (Eq. 27), S^g = c^dag sigma^g c / 2, J = 1: H = -2 sum S^g S^g, K = -2 in the S = sigma/2 form, twice the instance's K = -1 (scale 2). Total energies of the cluster: the per-site values -0.3970, -0.3977, -0.3926 the text compares with the thermodynamic -0.39365 are these totals over N. QMBL's flux-free free-Majorana energies of the 3 x 4 and 4 x 4 tori reproduce -9.54589 and -12.56409 (SWEEP.md, 2026-10-20).
-0.1942(3), VMC (PP)
Checked 2026-10-20 · source text of arXiv:1411.5198 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. −12.43 ± 0.02
Table I, row |ψMP⟩, column 4×4 unit cells; version read: arXiv text (sources/1411.5198.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Eq. (28) H_KH = 2 alpha H_K + (1 - alpha) J_H sum S.S at alpha = 1 (the text before Table I: 'the Kitaev model, where alpha = 1'), with H_K = -J sum S^g S^g (Eq. 27), S^g = c^dag sigma^g c / 2, J = 1: H = -2 sum S^g S^g, K = -2 in the S = sigma/2 form, twice the instance's K = -1 (scale 2). Total energies of the cluster: the per-site values -0.3970, -0.3977, -0.3926 the text compares with the thermodynamic -0.39365 are these totals over N. QMBL's flux-free free-Majorana energies of the 3 x 4 and 4 x 4 tori reproduce -9.54589 and -12.56409 (SWEEP.md, 2026-10-20).
-0.1867(5), VMC (PP)
Checked 2026-10-20 · source text of arXiv:1411.5198 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. −11.95 ± 0.03
Table I, row |ψpair⟩, column 4×4 unit cells; version read: arXiv text (sources/1411.5198.txt); the journal version was not reached from this session, to be read on the verification pass (RULES.md 8) | Eq. (28) H_KH = 2 alpha H_K + (1 - alpha) J_H sum S.S at alpha = 1 (the text before Table I: 'the Kitaev model, where alpha = 1'), with H_K = -J sum S^g S^g (Eq. 27), S^g = c^dag sigma^g c / 2, J = 1: H = -2 sum S^g S^g, K = -2 in the S = sigma/2 form, twice the instance's K = -1 (scale 2). Total energies of the cluster: the per-site values -0.3970, -0.3977, -0.3926 the text compares with the thermodynamic -0.39365 are these totals over N. QMBL's flux-free free-Majorana energies of the 3 x 4 and 4 x 4 tori reproduce -9.54589 and -12.56409 (SWEEP.md, 2026-10-20).