t-J ladder 2x11, J = 0.5, 2 holes

Exact energy and best values (rules §6)

exact	-0.5908993	ED 10.1103/PhysRevB.63.115120, · 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_↑ = 10, N_↓ = 10 on 22 sites (2 holes). Cluster: two-leg ladder of 11 rungs, periodic along the legs (arXiv:cond-mat/0010072: '2 x L ladder geometry with periodic boundary conditions').

lattice: ladder-2x11
sites: 22
boundary: periodic
t: 1
J: 0.5
N_up: 10
N_dn: 10
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
-0.5908993exact	0	n/a	n/a	n/a	ED peer reviewed	10.1103/PhysRevB.63.115120,		2001

How these numbers were read

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

-0.5908993, ED

Checked 2026-10-22 · source text of arXiv:cond-mat/0010072 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. − 12.99978

footnote 7: E_GS of the 2 x 11 ladder with two holes, sector (S = 0, K = (0, 0)), J/t = 0.5 (line 288); version read: arXiv text (sources/cond-mat-0010072.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. (3): H = J sum (S.S - n n / 4) on legs and rungs + t sum (c+c + h.c.) with t = -1, i.e. -|t| sum (c+c + h.c.), J/t = 0.5 'throughout'; footnote 7 prints total energies (E_GS, the ground state of the sector S = 0, K = (0, 0)). QMBL's diagonalization of the 2 x 11 ladder, unrestricted in momentum and spin, gives -12.9997844296 (checks/tj-ed-2026-10/).

Coverage

Newest published number here: 2001.

This instance as data

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