Heisenberg square 6x6, open

Heisenberg/square_36_O

Record

-0.6035218 E/N (S.S)

DMRG (bond dimension = 2048)

run script, no paper cited · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = ∑_⟨ij⟩ σ_i·σ_j

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

lattice: square
sites: 36
boundary: open
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 (3)

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
-0.6035218record	n/a	4.59e-4	2.2e-6	DMRG (bond dimension = 2048) VarBench reference run	run script, no paper cited	n/a
-0.59484(2)	2.5e-5	1.35e+1	6.6e-2	Jastrow baseline VarBench reference run	run script, no paper cited	n/a
-0.59365(2)	2.4e-5	1.23e+1	6.0e-2	RBM (alpha = 1) VarBench reference run	run script, no paper cited	n/a

Numerically exact (2)

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
-0.6035222(2)	1.7e-7	n/a	n/a	SSE QMC (stochastic series expansion), T -> 0 converged at beta/L = 32 and 64 preprint	Sandvik (2026)	2026
-0.6035218	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.

-0.6035222(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/N_b = 0.3621133(1) (magnitude, per bond, N_b = 60), L = 6, open

Table 2, "SSE data for L x L systems with open boundary conditions. The ground state energy is normalized by the number of interaction bonds N_b = 2(L^2 - L)", row L = 6. Printed as a magnitude; E/N = -(E0/N_b) N_b / N = -0.60352217 in S.S units, Pauli total = 4 N E/N. The L = 6 value agrees with the exact-diagonalization row on square_36_O to 3.3e-7 (2 sigma), and L = 10 and 16 reproduce the rows QMBL already quotes from this paper via arXiv:2605.13807.

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

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