J1-J2 square 6x6, J2 = 0.5

J1J2/square_36_P_0.5

Record

-0.503800(1) E/N (S.S)

RBM+PP with momentum (K=0), spin-parity (even S), and point-group (A1) projections, 16 hidden units

Nomura & Imada (2021) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

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

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

lattice: square
sites: 36
boundary: periodic
J2: 0.5
energies: 11

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 (10)

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
-0.503800(1)record	1.1e-6	3.70e-2	2.5e-4	RBM+PP with momentum (K=0), spin-parity (even S), and point-group (A1) projections, 16 hidden units	Nomura & Imada (2021)	2021
-0.50378(4)	4.0e-5	n/a	n/a	RBM wave function + 2-step Lanczos recursion preprint	Chen et al. (2022)	2022
-0.50376(3)	3.0e-5	n/a	n/a	RBM wave function + 1-step Lanczos recursion preprint	Chen et al. (2022)	2022
-0.5037597(6)	6.3e-7	1.91e-1	1.3e-3	RBM with momentum (K=0), spin-parity (even S), and point-group (A1) projections, 72 hidden units	Nomura (2021)	2021
-0.50364(2)	2.0e-5	n/a	n/a	RBM wave function preprint	Chen et al. (2022)	2022
-0.5025975	n/a	2.25e+0	1.5e-2	DMRG (bond dimension = 2048) VarBench reference run	run script, no paper cited	n/a
-0.50185(1)	1.0e-5	n/a	n/a	CNN quoted from another paper peer reviewed	Choo, Neupert & Carleo, Two-dime	n/a
-0.50116(2)	2.1e-5	5.42e+0	3.7e-2	VMC with projected BCS (Z2 spin liquid) VarBench reference run	run script, no paper cited	n/a
-0.48693(2)	2.4e-5	1.23e+1	9.0e-2	RBM (alpha = 1) VarBench reference run	run script, no paper cited	n/a
-0.47820(4)	3.6e-5	2.74e+1	2.1e-1	Jastrow baseline VarBench reference run	run script, no paper cited	n/a

Numerically exact (1)

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
-0.5038097	n/a	n/a	n/a	Exact diagonalization VarBench reference run	run script, no paper cited	n/a

How these numbers were read

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

-0.50378(4) — RBM wave function + 2-step Lanczos recursion

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

Reported as. -0.50378 (+/- 0.00004) per site in S.S units

Read from Table 2 of arXiv:2206.14307 (J1-J2 on the 6x6 square lattice, PBC, E/N in S.S units), extracted from the PDF with pypdf. p is the number of Lanczos steps.

-0.50376(3) — RBM wave function + 1-step Lanczos recursion

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

Reported as. -0.50376 (+/- 0.00003) per site in S.S units

Read from Table 2 of arXiv:2206.14307 (J1-J2 on the 6x6 square lattice, PBC, E/N in S.S units), extracted from the PDF with pypdf. p is the number of Lanczos steps.

-0.50364(2) — RBM wave function

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

Reported as. -0.50364 (+/- 0.00002) per site in S.S units

Read from Table 2 of arXiv:2206.14307 (J1-J2 on the 6x6 square lattice, PBC, E/N in S.S units), extracted from the PDF with pypdf. p is the number of Lanczos steps.

-0.50185(1) — CNN

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

Reported as. -0.50185 (+/- 0.00001) per site in S.S units

Read from Table 2 of arXiv:2206.14307 (J1-J2 on the 6x6 square lattice, PBC, E/N in S.S units), extracted from the PDF with pypdf. p is the number of Lanczos steps.

Coverage

Newest published number here: 2022. 4 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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