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Hubbard square 16x16, U = 8, n = 0.875, t12 (t2 = -0.1)

Record

-0.7370(1) E/site

HFPS (half-filled stripe + d-wave superconductivity)

Roth et al. (2025) · lowest unflagged energy published, a strict variational bound (rules §6)

The Hamiltonian

H = −t1 ∑⟨ij⟩,σ (c†iσcjσ + h.c.) −t2 ∑⟨⟨ij⟩⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓

t1 = 1, t2 = -0.1, U = 8, N↑ = N↓ = 112 on 256 sites.

This instance is a t12 variant: a next-nearest-neighbour hopping t2, written as in VarBench's Eq. (S6), so t2 is the t′ of the sources' H = −t ∑⟨ij⟩ − t′ ∑⟨⟨ij⟩⟩ + U ∑ ni↑ni↓. Couplings from the Hamiltonian each source prints (see the rows).

lattice
square
sites
256
boundary
periodic
Nf
112
U
8
t1
1
t2
-0.1
energies
2

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 (2)

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/sitedistance to recordσVar(E)V-score methodsourceyear
-0.7370record 0 1.0e-4 n/a n/a HFPS (half-filled stripe + d-wave superconductivity)
preprint
Roth et al. (2025) 2025
-0.7367 3.0e-4 1.0e-4 n/a n/a HFPS (filled stripe)
preprint
Roth et al. (2025) 2025

How these numbers were read

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

-0.7370(1) — HFPS (half-filled stripe + d-wave superconductivity)

Checked 2026-10-16 · 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. -0.7370(1)

Table V (App. D 'Supplementary data': 256-site 16x16 cluster, U=8, delta=1/8; columns Filled Stripe | Half-filled stripe + No SC | Half-filled stripe + SC); row t'=-0.1, column Half-filled stripe + SC; sources/2511.07566.txt line 1197; 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).

-0.7367(1) — HFPS (filled stripe)

Checked 2026-10-16 · 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. -0.7367(1)

Table V (App. D 'Supplementary data': 256-site 16x16 cluster, U=8, delta=1/8; columns Filled Stripe | Half-filled stripe + No SC | Half-filled stripe + SC); row t'=-0.1, column Filled Stripe; sources/2511.07566.txt line 1197; 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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