QMBLthe quantum many-body leaderboard

All instances / t-J

t-J square 8x8, J = 0.2, 14 holes

Best values (rules §6)

best variational -0.685(1) Power-Lanczos
10.1016/S0022-3697(01 · the lowest unflagged variational energy, a strict variational bound
best extrapolated -0.690(5) Power-Lanczos
10.1016/S0022-3697(01 · 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 = 0.2; the exchange term includes −ninj/4. N↑ = 25, N↓ = 25 on 64 sites (14 holes). Cluster: 8 x 8 torus (arXiv:cond-mat/0104067 Table I and 'periodic boundary condition', line 577).

lattice
square
sites
64
boundary
periodic
t
1
J
0.2
N_up
25
N_dn
25
nn_term
true
energies
15

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 (13)

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
-0.685best variational 0 1.3e-3 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.685tied with best variational at 2σ <1e-3 2.9e-3 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.683tied with best variational at 2σ 2.2e-3 1.1e-3 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.6820tied with best variational at 2σ 3.5e-3 8.0e-4 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.682tied with best variational at 2σ 3.6e-3 1.1e-3 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.6803 5.2e-3 6.0e-4 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.677 8.6e-3 1.2e-3 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.6768 8.7e-3 2.0e-4 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.6735 1.2e-2 9.0e-4 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.6709 1.5e-2 1.0e-4 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.6657 2.0e-2 6.0e-4 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.6573 2.8e-2 4.0e-4 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.6443 4.1e-2 1.0e-4 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001

Extrapolations (2)

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

E/sitedistance to class bestσVar(E)V-score methodsourcecodeyearcomment
-0.690best extrapolated 0 4.8e-3 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001
-0.688tied with best extrapolated at 2σ 2.3e-3 3.5e-3 n/a n/a Power-Lanczos
peer reviewed
10.1016/S0022-3697(01 2001

How these numbers were read

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

-0.690(5), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. −0.6904(48)

text below Fig. 6: E0 of the fit of the PL1 energies to infinite power, 50 electrons on 8 x 8, J/t = 0.2 (line 459); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.688(4), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. −0.6881(35)

text below Fig. 6: E0 of the fit of the PL0 energies to infinite power, 50 electrons on 8 x 8, J/t = 0.2 (line 458); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.685(1), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6855(13)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 8 (line 414); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.685(3), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6851(29)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL2, power 4 (line 412); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.683(1), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6833(11)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL2, power 2 (line 411); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.6820(8), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6820(8)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 6 (line 413); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.682(1), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6819(11)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL2, power 0 (line 410); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.6803(6), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6803(6)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 4 (line 412); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.677(1), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6769(12)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 8 (line 414); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.6768(2), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6768(2)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 2 (line 411); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.6735(9), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6735(9)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 6 (line 413); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.6709(1), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6709(1)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL1, power 0 (line 410); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.6657(6), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6657(6)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 4 (line 412); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.6573(4), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6573(4)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 2 (line 411); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

-0.6443(1), Power-Lanczos

Checked 2026-10-22 · source text of arXiv:cond-mat/0104067 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. -0.6443(1)

Table I, 50 electrons on 8 x 8, J/t = 0.2, PL0, power 0 (line 410); version read: arXiv text (sources/cond-mat-0104067.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); Table I is not labelled: read as energy per site in units of t, as the paper's e_h(x) and its comparison of -0.6855 with the per-site value -0.6825(23) of Hellberg & Manousakis, Phys. Rev. B 61, 11787, Table V (50 electrons on 64 sites, J/t = 0.2) show.

Coverage

Newest published number here: 2001.

This instance as data

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