The Hamiltonian
H = −t ∑⟨ij⟩,σ P(c†iσcjσ + h.c.)P + J ∑⟨ij⟩ (Si·Sj − ninj/4)
t-J model: P projects out doubly occupied sites, S = σ/2. t = 1, J = 0.4; the exchange term includes −ninj/4. N↑ = 28, N↓ = 28 on 64 sites (8 holes). Cluster: 8 x 8 torus (arXiv:cond-mat/0110460: '8 holes on the 8 x 8 lattice', PBC clusters).
- lattice
- square
- sites
- 64
- boundary
- periodic
- t
- 1
- J
- 0.4
- N_up
- 28
- N_dn
- 28
- nn_term
- true
- energies
- 3
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).
Strict variational upper bounds (1)
Energies that a variational state reached (VMC, DMRG and MPS at finite bond dimension, PEPS, NQS, VQE). Each is an upper bound on the ground-state energy.
Projected or fixed-node estimates (1)
Variational only within a constraint: fixed-node, constrained-path, GFMC on a trial state. Each depends on its node or constraint, so two of them are not cleanly comparable to each other or to strict bounds.
How these numbers were read
Where each number below was read, and how it was checked.
-0.671(1), VMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0110460 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. −0.671(1)
text: 8 holes on the 8 x 8 lattice, J/t = 0.4, energy per site (the zero variance extrapolation) (line 156); version read: arXiv text (sources/cond-mat-0110460.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 = J sum (S_i.S_j - n_i n_j / 4) - t sum c~+c~ + h.c.; energies per site in units of t ('best variational energy per site', 'E = ... t'), 8 holes on the 8 x 8 PBC cluster, J/t = 0.4.
-0.66672(6), FN-GFMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0110460 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. −0.66672(6)
text: 8 holes on the 8 x 8 lattice, J/t = 0.4, energy per site (best variational energy per site (FN+2LS)) (line 154); version read: arXiv text (sources/cond-mat-0110460.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 = J sum (S_i.S_j - n_i n_j / 4) - t sum c~+c~ + h.c.; energies per site in units of t ('best variational energy per site', 'E = ... t'), 8 holes on the 8 x 8 PBC cluster, J/t = 0.4.
-0.64266(8), VMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0110460 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. −0.64266(8)
text: 8 holes on the 8 x 8 lattice, J/t = 0.4, energy per site (the pure variational calculation) (line 157); version read: arXiv text (sources/cond-mat-0110460.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 = J sum (S_i.S_j - n_i n_j / 4) - t sum c~+c~ + h.c.; energies per site in units of t ('best variational energy per site', 'E = ... t'), 8 holes on the 8 x 8 PBC cluster, J/t = 0.4.