Heisenberg chain, 20 sites

Heisenberg/chain_20_P

Record

-0.4452193 E/N (S.S)

DMRG (max truncation error ~ 1.0E-13)

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.

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).

Grouped by what the number is. Ranking happens only inside the first group.

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
-0.4452193record	n/a	1.20e-10	1.9e-12	DMRG (max truncation error ~ 1.0E-13) VarBench reference run	run script, no paper cited	n/a
-0.44521887(6)	5.7e-8	5.34e-5	8.4e-7	RNN + translational symmetry VarBench reference run	run script, no paper cited	n/a
-0.44521861(9)	9.0e-8	1.28e-4	2.0e-6	RNN VarBench reference run	run script, no paper cited	n/a
-0.445182(4)	4.1e-6	4.88e-2	7.7e-4	VMC with projected fermions + Jastrow VarBench reference run	run script, no paper cited	n/a
-0.445049(5)	5.1e-6	1.76e-1	2.8e-3	RBM (alpha = 1) VarBench reference run	run script, no paper cited	n/a
-0.444397(6)	6.1e-6	2.42e-1	3.8e-3	Jastrow baseline VarBench reference run	run script, no paper cited	n/a

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
-0.4452193	0.0e+0	0.00e+0	0.0e+0	Exact diagonalization VarBench reference run	run script, no paper cited	n/a

No row here carries a publication year. Nothing has been added to this instance since the VarBench snapshot of 2024-10-22.