J1-J2 square 6x6, J2 = 1

J1J2/square_36_P_1

Record

-0.71429(1) E/N (S.S)

RBM wave function

Chen et al. (2022) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j + J₂ ∑_{⟨⟨ij⟩⟩} σ_i·σ_j

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

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).

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

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

E/N (S.S)	σ	Var(E)	V-score	method	source	year
-0.71429(1)record	1.0e-5	n/a	n/a	RBM wave function preprint	Chen et al. (2022)	2022
-0.71351(1)	1.0e-5	n/a	n/a	CNN quoted from another paper peer reviewed	Choo, Neupert & Carleo, Two-dime	n/a
-0.7130465	n/a	7.16e+0	2.4e-2	DMRG (bond dimension = 2048) VarBench reference run	run script, no paper cited	n/a
-0.70921(3)	3.1e-5	2.05e+1	7.1e-2	RBM (alpha = 1) VarBench reference run	run script, no paper cited	n/a
-0.70016(3)	3.5e-5	2.53e+1	9.0e-2	Jastrow baseline VarBench reference run	run script, no paper cited	n/a

Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established: the answer, not a claim about it.

E/N (S.S)	σ	Var(E)	V-score	method	source	year
-0.7143604	n/a	n/a	n/a	Exact diagonalization VarBench reference run	run script, no paper cited	n/a

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

-0.71429(1) — RBM wave function

Checked 2026-09-14 · arXiv PDF text extracted locally with pypdf, no LLM transcription

Reported as. -0.71429 (+/- 0.00001) per site in S.S units

Read from Table 5 of arXiv:2206.14307 (J1-J2 on 6x6 and 10x10 square lattices, PBC, E/N in S.S units), extracted from the PDF with pypdf.

-0.71351(1) — CNN

Checked 2026-09-14 · arXiv PDF text extracted locally with pypdf, no LLM transcription

Reported as. -0.71351 (+/- 0.00001) per site in S.S units

Read from Table 5 of arXiv:2206.14307 (J1-J2 on 6x6 and 10x10 square lattices, PBC, E/N in S.S units), extracted from the PDF with pypdf.

Newest published number here: 2022. 2 rows added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.