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All instances / Hubbard

Hubbard rectangular 6x16, U = 8, n = 0.875

No record

—

sampled rows carry no error bar (rules §6). Every row is still listed below.

The Hamiltonian

H = −t ∑⟨ij⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓

t = 1, U = 8, N↑ = N↓ = 42 on 96 sites.

lattice
rectangular-6x16
sites
96
boundary
periodic
Nf
42
U
8
energies
2

Stored as a total energy in the convention of VarBench; quoted here as E/site, which is what the papers report (how the conversion works).

Every published energy

Grouped by what the number is. Ranking happens only inside the first group.

Strict variational upper bounds (2)

Where the instance is not solved, the record is the lowest eligible energy in this group; where it is, the lowest eligible energy here is the best variational bound and the closest challenger to the exact one.

E/sitedistance to recordσVar(E)V-score methodsourceyear
-0.7486000 n/a n/a n/a n/a VMC (stripe λ = 8 + Jastrow + backflow)
peer reviewed ineligible: sampled, no error bar
arXiv:2111.04623 2022
-0.7439000 n/a n/a n/a n/a VMC (uniform + Jastrow + backflow)
peer reviewed ineligible: sampled, no error bar
arXiv:2111.04623 2022

How these numbers were read

Rows added after the VarBench import record where the number came from.

-0.7486000 — VMC (stripe λ = 8 + Jastrow + backflow)

Checked 2026-10-07 · source text of arXiv:2111.04623 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading

Reported as. -0.7486

Table 1 (U/t = 8, t' = 0), row Lx = 16, column 'Energy striped state (λ = 8)'; no per-value error bar | Energy per site in units of t on Lx x 6 ladders with 'periodic boundary conditions along both the x and the y directions', hole doping 1/8 (n = 7/8). 'The error bar on the energy is always smaller than 10^-4' is one statement for the whole table, not a per-value sigma.

-0.7439000 — VMC (uniform + Jastrow + backflow)

Checked 2026-10-07 · source text of arXiv:2111.04623 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading

Reported as. -0.7439

Table 1 (U/t = 8, t' = 0), row Lx = 16, column 'Energy uniform state'; no per-value error bar | Energy per site in units of t on Lx x 6 ladders with 'periodic boundary conditions along both the x and the y directions', hole doping 1/8 (n = 7/8). 'The error bar on the energy is always smaller than 10^-4' is one statement for the whole table, not a per-value sigma.

Coverage

Newest published number here: 2022. 2 rows added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

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