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All instances / t-J

t-J rectangular 6x16, periodic/open, J = 0.35, 8 holes

Best values (rules §6)

best variational -0.5470833 DMRG
10.1080/13642810110051782, · the lowest unflagged variational energy, a strict variational bound
best extrapolated -0.5484(5) DMRG
10.1080/13642810110051782, · the lowest unflagged extrapolated energy, an extrapolation, not a bound

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

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 = 0.35; the exchange term includes −ninj/4. N↑ = 44, N↓ = 44 on 96 sites (8 holes). Cluster: 16 x 6 cylinder, periodic along the 6-site direction, open along the 16-site direction (arXiv:cond-mat/0103096, lines 344-346 and Table I).

lattice
rectangular-6x16
sites
96
boundary
periodic/open
t
1
J
0.35
N_up
44
N_dn
44
nn_term
true
energies
4

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 (3)

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.

E/sitedistance to class bestσVar(E)V-score methodsourcecodeyearcomment
-0.5470833best variational 0 n/a n/a n/a DMRG
peer reviewed
10.1080/13642810110051782, 2001
-0.5464896 5.9e-4 n/a n/a n/a DMRG
peer reviewed
10.1080/13642810110051782, 2001
-0.544625 2.5e-3 n/a n/a n/a DMRG
peer reviewed
10.1080/13642810110051782, 2001

Extrapolations (1)

Zero-variance or bond-dimension extrapolations. These are not bounds: no ansatz reached the number.

E/sitedistance to class bestσVar(E)V-score methodsourcecodeyearcomment
-0.5484best extrapolated 0 5.2e-4 n/a n/a DMRG
peer reviewed
10.1080/13642810110051782, 2001

How these numbers were read

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

-0.5484(5), DMRG

Checked 2026-10-22 · source text of arXiv:cond-mat/0103096 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. −52.65 ± 0.05

Table I, 16 x 6, J = 0.35, 8 holes, cylindrical boundaries, estimate extrapolated to zero truncation error (line 789); version read: arXiv text (sources/cond-mat-0103096.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, J = 0.35; Table I prints the total energy E of the 16 x 6 system with 8 holes and cylindrical boundary conditions.

-0.5470833, DMRG

Checked 2026-10-22 · source text of arXiv:cond-mat/0103096 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. −52.520

Table I, 16 x 6, J = 0.35, 8 holes, cylindrical boundaries, SU(2) basis, m = 1200 (line 788); version read: arXiv text (sources/cond-mat-0103096.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, J = 0.35; Table I prints the total energy E of the 16 x 6 system with 8 holes and cylindrical boundary conditions.

-0.5464896, DMRG

Checked 2026-10-22 · source text of arXiv:cond-mat/0103096 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. −52.463

Table I, 16 x 6, J = 0.35, 8 holes, cylindrical boundaries, SU(2) basis, m = 800 (line 786); version read: arXiv text (sources/cond-mat-0103096.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, J = 0.35; Table I prints the total energy E of the 16 x 6 system with 8 holes and cylindrical boundary conditions.

-0.544625, DMRG

Checked 2026-10-22 · source text of arXiv:cond-mat/0103096 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. −52.284

Table I, 16 x 6, J = 0.35, 8 holes, cylindrical boundaries, SU(2) basis, m = 500 (line 784); version read: arXiv text (sources/cond-mat-0103096.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, J = 0.35; Table I prints the total energy E of the 16 x 6 system with 8 holes and cylindrical boundary conditions.

Coverage

Newest published number here: 2001.

This instance as data

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