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All instances / J1-J2

J1-J2 square 20x20, J2 = 0.5

J1J2/square_400_P_0.5

Record

-0.4967987(6) E/N (S.S)

CNN-MPS (h,D,l)=(32,15,20)

Fan et al. (2026) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑⟨ij⟩ σi·σj + J2⟨⟨ij⟩⟩ σi·σj

J1 = 1, J2 = 0.5, nearest and next-nearest neighbours, written with Pauli matrices.

lattice
square
sites
400
boundary
periodic
J2
0.5
energies
2

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).

Every published energy

Grouped by what the number is. Ranking happens only inside the first group.

Strict variational upper bounds (2)

The record is the lowest eligible energy in this group, and only this group.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.4967987(6)record 6.0e-7 n/a n/a CNN-MPS (h,D,l)=(32,15,20)
preprint
Fan et al. (2026) 2026
-0.496732(1) 1.0e-6 n/a n/a ViT with symmetry restoration
preprint
Viteritti et al. (2026) 2026

How these numbers were read

Rows added after the VarBench import record where the number came from.

-0.4967987(6) — CNN-MPS (h,D,l)=(32,15,20)

Checked 2026-09-13 · arXiv HTML parsed locally, no LLM transcription

Reported as. -0.4967987 (+/- 6e-7) per site in S.S units

Read from Table 1 of arXiv:2603.14425 (square-lattice J1-J2 at J2/J1=0.5, PBC, E per site in S.S units), parsed from the arXiv HTML. 20x20; no VarBench instance existed for this size.

-0.496732(1) — ViT with symmetry restoration

Checked 2026-09-13 · arXiv HTML parsed locally, no LLM transcription

Reported as. -0.496732 (+/- 0.000001) per site in S.S units

Read from Table 1 of arXiv:2603.14425 (square-lattice J1-J2 at J2/J1=0.5, PBC, E per site in S.S units), parsed from the arXiv HTML. Listed in Table 1 as the L=20 ViT 2026 value; matches the source paper's own symmetry-restoration sequence.

Coverage

Newest published number here: 2026. 2 rows added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

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