Hubbard square 12x12, U = 6, n ≈ 0.8333

Record

-0.92516(5) E/site

HFPS (GCNN; lowest energy over the initialisations tried)

Roth et al. (2025) · 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 = 6, N_↑ = N_↓ = 60 on 144 sites.

lattice: square
sites: 144
boundary: periodic
Nf: 60
U: 6
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. On a solved instance the exact energy is the record; otherwise the lowest unflagged energy of any group holds it (rules §6).

Strict variational upper bounds (1)

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/site	distance to record	σ	Var(E)	V-score	method	source	year
-0.92516record	0	5.0e-5	n/a	n/a	HFPS (GCNN; lowest energy over the initialisations tried) preprint	Roth et al. (2025)	2025

How these numbers were read

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

-0.92516(5), HFPS (GCNN; lowest energy over the initialisations tried)

Checked 2026-10-22 · source text of arXiv:2511.07566 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. -0.92516(5)

Table VII (App. D, lowest-energy wavefunction on the 144-site cluster at various U; t'=0, delta=1/6 from Fig. 4 caption and Sec. IV C); row U=6; sources/2511.07566.txt line 1225; version read: arXiv v1 (sources/2511.07566.txt); no journal version (Crossref, arXiv abs page) | Eq. (1): H = U sum n_up n_dn - sum t_xx' c+c, t_xx' = t' on next-nearest bonds, periodic; Table V: 16x16, U = 8, doping 1/8, energy per site. The d-wave field Delta_0 enters only the mean-field Hamiltonian of the initial orbitals (Eq. 5, App. D).

Coverage

Newest published number here: 2025.

This instance as data

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