Hubbard rectangular 4x12, U = 8, n = 0.875

Record

-0.76608(1) E/site

HFPS (GCNN)

Chen et al. (2026) · lowest unflagged energy published, a strict variational bound (rules §6)

The Hamiltonian

H = −t ∑_⟨ij⟩,σ (c^†_iσc_jσ + h.c.) + U ∑_i n_i↑n_i↓

t = 1, U = 8, N_↑ = N_↓ = 21 on 48 sites.

lattice: rectangular-4x12
sites: 48
boundary: periodic
Nf: 21
U: 8
energies: 1

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. Where the instance is not solved, the lowest unflagged energy of any group is the record.

Strict variational upper bounds (1)

Where the instance is not solved, the record is the lowest unflagged energy in this group or among the projected and extrapolated ones, with or without an error bar; where it is solved, the exact energy is the record and the lowest of these is the closest challenger.

E/site	distance to record	σ	Var(E)	V-score	method	source	year
-0.76608record	0	1.0e-5	n/a	n/a	HFPS (GCNN) peer reviewed	Chen et al. (2026)	2026

How these numbers were read

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

-0.76608(1) — HFPS (GCNN)

Checked 2026-10-16 · source text of arXiv:2507.10705 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. -0.76608(1)

TABLE IV, 12x4 row; sources/2507.10705.txt line 970; version read: arXiv v1 (sources/2507.10705.txt); PNAS copy not reached (Cloudflare 403, 2026-10-16) | Eq. (15): H = -t sum_<ij> + U sum n_up n_dn, t = 1, t' = 0, periodic; all tables per site (E/Nsite).

Coverage

Newest published number here: 2026.

This instance as data

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