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

Hubbard/rectangular-8x16_128_P_56_8

No record

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

The Hamiltonian

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

t = 1, U = 8, N = N = 56 on 128 sites.

lattice
rectangular-8x16
sites
128
boundary
periodic
Nf
56
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)

The record is the lowest eligible energy in this group, and only this group.

E/siteσVar(E)V-score methodsourceyear
-0.7568000 n/a n/a n/a Tensor-Backflow + 1 Lanczos step (NN backflow, direct optimization, Ep = 1)
preprint ineligible: sampled, no error bar
Investigating the Fermi-Hubbard n/a
-0.7529000 n/a n/a n/a Tensor-Backflow (NN backflow, direct optimization, Ep = 0)
preprint ineligible: sampled, no error bar
Investigating the Fermi-Hubbard n/a

How these numbers were read

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

-0.7568000 ○ — Tensor-Backflow + 1 Lanczos step (NN backflow, direct...

Checked 2026-09-15 · source text of arXiv:2507.01856 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.7568

Table V of arXiv:2507.01856 (pypdf layout text, line 399), 8x16, t' = 0, NN backflow, column Ep = 1 | n = 0.875, U = 8 (Table V caption); PBC: the 8x16 Ep = 1 value equals Table II's 8x16 PBC row, and Figs. 4 and 8 state the 8x32 lattice is under PBC

-0.7529000 ○ — Tensor-Backflow (NN backflow, direct optimization, Ep = 0)

Checked 2026-09-15 · source text of arXiv:2507.01856 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; parsed by column from the primary table

Reported as. -0.7529

Table V of arXiv:2507.01856 (pypdf layout text, line 399), 8x16, t' = 0, NN backflow, column Ep = 0 | n = 0.875, U = 8 (Table V caption); PBC: the 8x16 Ep = 1 value equals Table II's 8x16 PBC row, and Figs. 4 and 8 state the 8x32 lattice is under PBC

Coverage

No row here carries a publication year. 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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