QMBLthe quantum many-body leaderboard

All instances / J1-J2

J1-J2 square 12x12, J2 = 0.5

J1J2/square_144_P_0.5

Record

-0.496791(4) E/N (S.S)

mVMC + RBM (as quoted)

Roth et al. (2022) · 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
144
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
-0.496791(4)record 4.0e-6 n/a n/a mVMC + RBM (as quoted)
quoted from another paper
Roth et al. (2022) 2022
-0.496769(9) 9.0e-6 n/a n/a GCNN (deep group-convolutional network)
peer reviewed
Roth et al. (2022) 2022

How these numbers were read

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

-0.496791(4) — mVMC + RBM (as quoted)

Checked 2026-09-15 · source text of arXiv:2211.07749 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.496791(4)

Table I of arXiv:2211.07749 (line 185), J2/J1 = 0.5, 12x12, Ref. [7] column | E/J1 per site in S.S units on the L x L periodic torus

-0.496769(9) — GCNN (deep group-convolutional network)

Checked 2026-09-15 · source text of arXiv:2211.07749 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.496769(9)

Table I of arXiv:2211.07749 (pypdf layout text, line 185), J2/J1 = 0.5, 12x12, Our work | E/J1 per site in S.S units on the L x L periodic torus (caption: units of J1/spin)

Coverage

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

This instance as data

JSON · source file on GitHub · open an issue about this instance