Heisenberg square 12x12

Heisenberg/square_144_P

No record

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solved exactly (rules §6). Every row is still listed below.

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j

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

lattice: square
sites: 144
boundary: periodic
energies: 1

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.

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
-0.67068192(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.

-0.67068192(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 = -0.67068192(2) per spin (S.S), L = 12, 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 = 12. Pauli total = 4 N e0. The L = 6 value agrees with the exact-diagonalization row on square_36_P to 1.6e-8.

Coverage

Newest published number here: 2026. 1 row 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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