The Hamiltonian
H = −t ∑⟨ij⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓
t = 1, U = 8, N↑ = N↓ = 7 on 16 sites.
- lattice
- square
- sites
- 16
- boundary
- periodic
- Nf
- 7
- U
- 8
- energies
- 2
Stored as a total energy; quoted here as
E/site, which is what the papers report
(how the conversion works).
How these numbers were read
Where each number below was read, and how it was checked.
-0.74177(5), HFPS (GCNN)
Checked 2026-10-22 · 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. -0.74177(5)
TABLE IV, 4x4 row; sources/2507.10705.txt line 968; 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).
-0.7409(1), HFDS (full hidden sub-matrix)
Checked 2026-10-22 · source text of arXiv:2111.10420 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. -0.7409(1)
Appendix H Table IV, L=4, column "Energy per site HFDS (PBC-PBC)"; sources/2111.10420.txt line 1253; version read: arXiv:2111.10420v2 text, Appendix H (sources/2111.10420.txt); the PNAS SI (Cloudflare 403 on 2026-10-16) was read for this paper's earlier rows on 2026-09-29 | Eq. (1): H = -sum t_ij (c+c + h.c.) + U sum n_up n_dn, t = 1. Tables I-III print totals on the 4x4 torus (ED -17.698 on 16 sites); Tables IV and V print 'energy per site'. The rounded U of the tables (0.6, 2.15, 3.6, 7.75) are the grid 10^(k/9): QMBL's ED at U = 0.59948425 gives -19.47476333 and at 2.15443469 (n = 1/2) -18.40532088, the printed ED values, against -19.47434179 at U = 0.6 and -18.40534078 at U = 2.1544 (checks/hubbard-u-labels/results-2026-10-16/, run_fermions.mjs).