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Heisenberg square 10x10

Heisenberg/square_100_P

Record

-0.67155260(3) E/N (S.S)

CNN + MinSR

Chen & Heyl (2023) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑⟨ij⟩ σi·σj

Nearest-neighbour Heisenberg antiferromagnet, J = 1, written with Pauli matrices.

lattice
square
sites
100
boundary
periodic
energies
12

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)σVar(E)V-score methodsourceyear
-0.67155260(3)record 3.0e-8 n/a n/a CNN + MinSR
quoted from another paper
Chen & Heyl (2023) 2023
-0.671519(4) 4.0e-6 n/a n/a RBM + Lanczos recursion Chen et al. (2022) 2022
-0.67151(2) 2.0e-5 n/a n/a 2D RNN wavefunction (best variational)
peer reviewed
Moss et al. (2025) 2025
-0.67140(1) 1.3e-5 9.20e-2 1.3e-4 RNN + translational symmetry
VarBench reference run
run script, no paper cited n/a
-0.6713500 n/a n/a n/a CNN
quoted from another paper ineligible: sampled, no error bar
Choo, Neupert & Carleo, Two-dime n/a
-0.671134(1) 1.3e-6 5.41e-1 7.5e-4 RNN
VarBench reference run
run script, no paper cited n/a
-0.66935(1) 1.0e-5 1.22e+1 1.7e-2 VMC with fermions (flux+neel+Jastrow)
VarBench reference run
run script, no paper cited n/a
-0.6648562 n/a 4.25e+1 6.0e-2 DMRG (bond dimension = 1024)
VarBench reference run
run script, no paper cited n/a
-0.66443(2) 1.5e-5 3.71e+1 5.3e-2 RBM (alpha = 1)
VarBench reference run
run script, no paper cited n/a
-0.66421(1) 1.4e-5 3.20e+1 4.5e-2 Jastrow baseline
VarBench reference run
run script, no paper cited n/a

Extrapolations (1)

Zero-variance, bond-dimension or Trotter-error extrapolations. Not a bound: no ansatz ever reached the number, so it cannot hold the record.

E/N (S.S)σVar(E)V-score methodsourceyear
-0.6715950(5) 5.0e-7 n/a n/a 2D RNN wavefunction, zero-variance extrapolation
peer reviewed
Moss et al. (2025) 2025

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)σVar(E)V-score methodsourceyear
-0.67155266(2) 2.0e-8 n/a n/a SSE QMC (stochastic series expansion), T -> 0 converged at beta/L = 32 and 64
preprint
Sandvik (2026) 2026

How these numbers were read

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

-0.6715950(5) — 2D RNN wavefunction, zero-variance extrapolation

Checked 2026-09-14 · arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription

Reported as. -0.671595 (+/- 5e-7) per site in S.S units

Read from Table 5 of arXiv:2502.17144 (SLAHM, E/N in S.S units), parsed from the arXiv HTML. Zero-variance extrapolation, not an achieved energy (RULES.md 4).

-0.67155266(2) — SSE QMC (stochastic series expansion), T -> 0 converged at...

Checked 2026-09-15 · arXiv HTML parsed locally, one value per table cell; no LLM transcription

Reported as. e0 = -0.67155266(2) per spin (S.S), L = 10, periodic

Table 1, "Results for different system sizes computed at inverse temperature beta/L = 64 for L > 30 and averaged over beta/L = 32 and beta/L = 64 simulations for L <= 30", column e0, row L = 10. Pauli total = 4 N e0. The L = 6 value agrees with the exact-diagonalization row on square_36_P to 1.6e-8.

-0.67155260(3) — CNN + MinSR

Checked 2026-09-14 · arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription

Reported as. -0.6715526 (+/- 3e-8) per site in S.S units

Read from Table 5 of arXiv:2502.17144 (SLAHM, E/N in S.S units), parsed from the arXiv HTML. Row "VMC - CNN+MinSR [12]" = Chen & Heyl, Nat. Phys. 20, 1476 (2024).

-0.671519(4) — RBM + Lanczos recursion

Checked 2026-09-14 · found in the citing paper's comparison table, then confirmed in the primary source's own PDF (pypdf); no LLM transcription

Reported as. -0.671519 (+/- 0.000004) per site in S.S units

Read from Table 5 of arXiv:2502.17144 (SLAHM, E/N in S.S units), parsed from the arXiv HTML. Row "RBM+Lanczos [40]" = arXiv:2206.14307. CONFIRMED IN PRIMARY SOURCE - arXiv:2206.14307 Table 4: "10x10 0.671549(4) 5.3124(3) -0.671519(4) 5.38(6)" - Energy(QMC) beside Energy(RBM).

-0.67151(2) — 2D RNN wavefunction (best variational)

Checked 2026-09-14 · arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription

Reported as. -0.67151 (+/- 0.00002) per site in S.S units

Read from Table 5 of arXiv:2502.17144 (SLAHM, E/N in S.S units), parsed from the arXiv HTML. Row "This work (best RNN)".

-0.6713500 ○ — CNN

Checked 2026-09-14 · arXiv HTML parsed locally from a benchmark comparison table, no LLM transcription

Reported as. -0.67135 per site in S.S units

Read from Table 5 of arXiv:2502.17144 (SLAHM, E/N in S.S units), parsed from the arXiv HTML. Row "CNN [33]" = Phys. Rev. B 100, 125124 (2019). No error bar given.

Coverage

Newest published number here: 2026. 6 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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