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Heisenberg square 14x14

Heisenberg/square_196_P

Record

-0.668346(8) E/N (S.S)

VMC with fermions (flux+neel+Jastrow)

run script, no paper cited · 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
196
boundary
periodic
energies
5

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 (4)

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

E/N (S.S)σVar(E)V-score methodsourceyear
-0.668346(8)record 7.7e-6 2.21e+1 1.6e-2 VMC with fermions (flux+neel+Jastrow)
VarBench reference run
run script, no paper cited n/a
-0.66381(1) 1.0e-5 6.37e+1 4.6e-2 RBM (alpha = 1)
VarBench reference run
run script, no paper cited n/a
-0.66256(1) 1.0e-5 6.67e+1 4.8e-2 Jastrow baseline
VarBench reference run
run script, no paper cited n/a
-0.6586622 n/a 1.28e+2 4.8e-2 DMRG (bond dimension = 512)
flagged: dof-mismatch 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)σVar(E)V-score methodsourceyear
-0.67023225(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

Flagged rows

A flag withholds the record and nothing else: the row stays listed, in rank order. Rules §10 is how a flag is lifted or upheld.

dof-mismatch — DMRG (bond dimension = 512), -0.6586622

Finding. Row stores dof = 100 on a 196-site instance. Upstream typo; the V-score derived from it would be wrong by a factor of ~2.

How these numbers were read

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

-0.67023225(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 = -0.67023225(2) per spin (S.S), L = 14, 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 = 14. 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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