t-J square, 32 sites, J = 0.3, t′ = 0.3, t″ = -0.2, 2 holes

Exact energy and best values (rules §6)

exact	-0.5188028	ED 10.1103/PhysRevB.73.075104, · 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 −t′ ∑_{⟨⟨ij⟩⟩,σ} P(c^†_iσc_jσ + h.c.)P −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 = 0.3, t′ = 0.3, t″ = -0.2; the exchange term includes −n_in_j/4. N_↑ = 15, N_↓ = 15 on 32 sites (2 holes). Cluster: square-shaped periodic cluster of 32 sites, edge vectors (4, 4) and (4, -4) (RULES.md 2.1); the source states 'a square lattice with 32 sites and periodic boundary conditions'.

lattice: square
sites: 32
boundary: periodic
t: 1
J: 0.3
t2: 0.3
t3: -0.2
N_up: 15
N_dn: 15
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
-0.5188028exact	0	n/a	n/a	n/a	ED peer reviewed	10.1103/PhysRevB.73.075104,		2006

How these numbers were read

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

-0.5188028, ED

Checked 2026-10-22 · source text of arXiv:cond-mat/0508035 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. −16.601689

Table I, E_Nc for Nc = 2 charge carriers of the electron-doped model (t = -1, t' = 0.3, t'' = -0.2, J = 0.3) (line 69); version read: arXiv text (sources/cond-mat-0508035.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 = -sum t_ij (c~+c~ + h.c.) + J sum_nn (S_i.S_j - n_i n_j / 4); the electron-doped model is Eq. (1) with t = -1, t' = 0.3, t'' = -0.2, J = 0.3 in the hole operators of the electron-hole transformation (lines 98-114), Nc charge carriers on 32 sites: a t-J model with 32 - Nc particles and no double occupancy. The cluster is bipartite, so the gauge c_i -> (-1)^i c_i takes t = -1 to t = 1 and leaves t' and t'' (same-sublattice hops): t' = 0.3, t'' = -0.2 in the form -t' sum - t'' sum. Total energies (Table I). Convention check: at half filling the source prints E00 = -11.329720 (Table I caption, sources/cond-mat-0508035.txt line 65); with J = 0.3 and -n_i n_j / 4 on the 64 bonds this is 0.3 (E_S.S - 16), so E_S.S / 32 = -0.6801792, the 32-site Heisenberg energy per site -0.680179 printed by Schulz, Ziman & Poilblanc (arXiv:cond-mat/9402061 Table II, J2 = 0.00, column 32; sources/cond-mat-9402061.txt line 1642). Without the -n_i n_j / 4 term E00 would be -6.53.

Coverage

Newest published number here: 2006.

This instance as data

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