t-J ladder 3x6, antiperiodic legs, J = 0.5, 1 hole

Exact energy and best values (rules §6)

exact	-0.5781986	ED 10.1103/PhysRevB.56.14655, · the instance is solved

Energies as E/site. Classes are different claims and are not ranked against each other.

The Hamiltonian

H = −t ∑_⟨ij⟩,σ P(c^†_iσc_jσ + h.c.)P + J ∑_⟨ij⟩ (S_i·S_j − n_in_j/4)

t-J model: P projects out doubly occupied sites, S = σ/2. t = 1, J = 0.5; the exchange term includes −n_in_j/4. N_↑ = 9, N_↓ = 8 on 18 sites (1 hole). Cluster: three-leg ladder of 6 rungs, isotropic (t' = t, J' = J on the rungs), antiperiodic along the legs and open across them (arXiv:cond-mat/9706147 Table I); QMBL's diagonalization reproduces both energies (checks/tj-ed-2026-10/).

lattice: ladder-3x6
sites: 18
boundary: antiperiodic legs
t: 1
J: 0.5
N_up: 9
N_dn: 8
nn_term: true
energies: 1

Stored as a total energy; quoted here as E/site, which is what the papers report (how the conversion works).

Every published energy

Grouped by what the number is. The exact energy comes first where there is one; in every other group the lowest unflagged energy is its best value, and each row's distance is to that best (rules §6).

Numerically exact (1)

Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established. An exact energy is shown first, before the best of each other class. QMC is exact only within its error bar, which it must state, and reads exact (stochastic); an exact diagonalization outranks it. For a diagonalization resolved by symmetry sector only the ground state's sector is listed; the lowest energies of the other sectors are the instance's spectrum, in its JSON, and are not shown as the exact energy.

E/site	distance to class best	σ	Var(E)	V-score	method	source	code	year	comment
-0.5781986exact	0	n/a	n/a	n/a	ED peer reviewed	10.1103/PhysRevB.56.14655,		1997

How these numbers were read

Where each number below was read, and how it was checked.

-0.5781986, ED

Checked 2026-10-22 · source text of arXiv:cond-mat/9706147 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; first reading and an adversarial second reading (2026-10-22)

Reported as. -10.40757

Table I, 3 x 6 isotropic ladder, 1 hole, lowest entry of the column (k = π/2, R = -1) (line 609); version read: arXiv text (sources/cond-mat-9706147.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Eq. (1): H = -t sum P(c+c + h.c.)P - t' sum (rungs) + J sum (S.S - n n / 4) + J' sum (rungs), isotropic t' = t, J' = J, J/t = 0.5; Table I prints total energies per symmetry sector; the lowest of each column is the ground state, and QMBL's diagonalization of the 3 x 6 ladder with antiperiodic legs gives -10.4075745288 (1 hole) and -11.8068024851 (2 holes).

Coverage

Newest published number here: 1997.

This instance as data

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