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 = 0.3; the exchange term includes −ninj/4. N↑ = 11, N↓ = 11 on 26 sites (4 holes). Cluster: square-shaped periodic cluster of 26 sites, edge vectors (5, 1) and (-1, 5), the only square-shaped cluster with N = 26 (RULES.md 2.1). Inferred, not printed: arXiv:cond-mat/0606659 describes its clusters as 'a square lattice with L sites and periodic boundary conditions rotated by 45 degrees such that L = 2l^2, l being an odd integer', which does not include L = 26, and states no other shape; arXiv:cond-mat/0009149 lists 13 shells for its 26-site cluster, as the (5, 1) cluster has (SWEEP.md, 2026-10-22). Confirmed by QMBL's diagonalization of the (5, 1) cluster (checks/tj-exact-recompute-2026-10/, 2026-10-23), which reproduces every printed 26-site exact energy to its printed digits: with 2 holes in all 14 momentum and C4 sectors, with 4 holes in the zero-momentum, C4-even sector, the lowest of the 1 to 6 of 14 sectors computed.
- lattice
- square
- sites
- 26
- boundary
- periodic
- t
- 1
- J
- 0.3
- N_up
- 11
- N_dn
- 11
- nn_term
- true
- energies
- 12
Stored as a total energy; quoted here as
E/site, which is what the papers report
(how the conversion works).
How these numbers were read
Where each number below was read, and how it was checked.
-0.6426164, ED
Checked 2026-10-22 · source text of arXiv:cond-mat/0009149 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. -0.64262
Table I, N = 22, L = 26, J/t = 0.3, column Exact; the acknowledgements (lines 829-831) credit D. Poilblanc's unpublished 26-site data (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.
-0.6387(1), VMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0009149 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. -0.6387(1)
Table I, N = 22, L = 26, J/t = 0.3, column Best SR (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.
-0.6381(1), VMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0009149 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. -0.6381(1)
Table I, N = 22, L = 26, J/t = 0.3, column VMC+2LS (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.
-0.6371(1), FN-GFMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0009149 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. -0.6371(1)
Table I, N = 22, L = 26, J/t = 0.3, column VMC+LS+FN (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.
-0.6332(1), VMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0009149 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. -0.6332(1)
Table I, N = 22, L = 26, J/t = 0.3, column VMC+LS (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.
-0.62958(3), FN-GFMC (Pfaffian)
Checked 2026-10-22 · source text of arXiv:cond-mat/0606659 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. -0.62958(3)
Table II, J/t = 0.3, column Ẽ_Ψ0^γ=0 (Eq. 15, Pfaff) (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).
-0.6277(1), FN-GFMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0009149 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. -0.6277(1)
Table I, N = 22, L = 26, J/t = 0.3, column VMC+FN (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.
-0.62754(1), FN-GFMC (Pfaffian)
Checked 2026-10-22 · source text of arXiv:cond-mat/0606659 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. -0.62754(1)
Table II, J/t = 0.3, column E_FN^Pfaff (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).
-0.62752(1), FN-GFMC (RVB)
Checked 2026-10-22 · source text of arXiv:cond-mat/0606659 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. -0.62752(1)
Table II, J/t = 0.3, column E_FN^RVB (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).
-0.61478(1), VMC (Pfaffian)
Checked 2026-10-22 · source text of arXiv:cond-mat/0606659 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. -0.61478(1)
Table II, J/t = 0.3, column E_VMC^Pfaff (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).
-0.6138(1), VMC (Gutzwiller)
Checked 2026-10-22 · source text of arXiv:cond-mat/0009149 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. -0.6138(1)
Table I, N = 22, L = 26, J/t = 0.3, column VMC (line 1050); version read: arXiv text (sources/cond-mat-0009149.txt); the journal version was not reached from this session (the publisher returned 403), to be read on the verification pass (RULES.md 8) | Table I: 'Energy per site in the t-J model', N electrons on L sites, t = 1. The Hamiltonian is not printed; its exact column on L = 26 (-0.64262, -0.78812, -1.17493) is the Lanczos column of Lugas, Spanu, Becca & Sorella, Phys. Rev. B 74, 165122, Table II, whose Eq. (1) includes -n_i n_j / 4 and periodic boundaries, so the 26-site rows share that instance.
-0.61372(1), VMC (RVB)
Checked 2026-10-22 · source text of arXiv:cond-mat/0606659 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. -0.61372(1)
Table II, J/t = 0.3, column E_VMC^RVB (line 393); version read: arXiv text (sources/cond-mat-0606659.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 (c+c + h.c.) + J sum (S_i.S_j - n_i n_j / 4), t = 1; Tables I and II print E/L, L = 26, for 2 and 4 holes. The Lanczos column agrees with the exact column of Sorella, Phys. Rev. B 64, 024512, Table I at J/t = 0.3, 0.5, 1.0 (4 holes), which fixes one convention for both papers (that paper is Sorella, Phys. Rev. B 64, 024512).