The Hamiltonian
H = ∑⟨ij⟩ σi·σj + J2 ∑⟨⟨ij⟩⟩ σi·σj
J1 = 1, J2 = 0.48, nearest and next-nearest neighbours, written with Pauli matrices.
- lattice
- square
- sites
- 256
- boundary
- periodic
- J2
- 0.48
- energies
- 3
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).
How these numbers were read
Rows added after the VarBench import record where the number came from.
-0.5014700 — CNN (CNN1, 1 Lanczos step)
Checked 2026-10-07 · source text of arXiv:2204.07816 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. −0.501 47
Table 1 of the published article ('achieved by CNN1 with 106 529 parameters. The values are obtained by the Lanczos step with p = 1'), row 16 x 16, column 0.48; no error bar printed | Energy per site in S.S units on periodic lattices (abstract: 'rectangular lattices within periodic boundary conditions'); its 10x10 cells at J2 = 0.50 and 0.60 equal the rows QMBL already carries.
-0.5012200 — CNN
Checked 2026-10-07 · source text of arXiv:2108.13830 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -0.50122
Table 4 ('Energies for varied J2/J1 && system scales'), row 16 x 16, column 0.48; no error bar printed | Energy per site in S.S units, periodic boundary conditions (text: 'periodic boundary condition'); the 10x10 and 16x16 cells at J2 = 0.50 equal the rows QMBL already carries from this table.
-0.5008(2) — TPS (extrapolated: χ → ∞ (contraction dimension Dc, linear...
Checked 2026-10-07 · source text of arXiv:1112.3331 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -0.5008(2)
Table I, row J2 = 0.48, column L=16 | Energy per site in S.S units; the table's own L = 4 and L = 6 ED columns equal QMBL's exact rows. The finite-size values are extrapolated linearly in 1/Dc^2 (text), so they are not upper bounds.