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Transverse-field Ising chain, 32 sites, h = 0.5

TFIsing/chain_32_P_0.5

Record

-1.0635444 E/N (Pauli)

DMRG (bond dimension = 24)

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

The Hamiltonian

H = −∑⟨ij⟩ σziσzj − h ∑i σxi

Transverse field h = 0.5. Already in Pauli operators, with no S·S term to rescale, so the per-site energy is E/N.

lattice
chain
sites
32
boundary
periodic
h
0.5
energies
5

Stored as a total energy in the convention of VarBench; quoted here as E/N (Pauli), 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 (Pauli)σVar(E)V-score methodsourceyear
-1.063551(2) 1.7e-6 3.24e-3 8.9e-5 RBM (alpha = 1)
flagged: below-exact-suspected VarBench reference run
run script, no paper cited n/a
-1.0635444record n/a 1.60e-10 4.4e-12 DMRG (bond dimension = 24)
VarBench reference run
run script, no paper cited n/a
-1.0635431(6) 5.9e-7 3.50e-4 9.7e-6 Symmetric FFN, Relu, 32 features per translation
VarBench reference run
run script, no paper cited n/a
-1.06305(1) 1.0e-5 1.17e-1 3.2e-3 Jastrow baseline
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 (Pauli)σVar(E)V-score methodsourceyear
-1.0635444 0.0e+0 0.00e+0 0.0e+0 Exact Solution
VarBench reference run
run script, no paper cited n/a

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.

below-exact-suspected — RBM (alpha = 1), -1.063551(2)

Finding. 3.8 sigma below the exact solution, same method string and same signature as the two 10-site rows. Not directly reproduced: 32 sites cannot be summed exactly, so the full-summation argument does not apply here.

Coverage

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

This instance as data

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