All instances / Hubbard
Hubbard chain, 14 sites, U = 4.64158883, n ≈ 0.5714
Exact energy and best values
(rules §6)
Energies as E/site. Classes are different claims and are not ranked against each other.
The Hamiltonian
H = −t ∑⟨ij⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓
t = 1, U = 4.64158883, N↑ = N↓ = 4 on 14 sites.
Upstream this instance is Hubbard/chain_14_P_4_4.64158882. The name's 4.64158882 misrounds the coupling of this Hamiltonian, 4.6415888336 (10^(6/9)). The exact diagonalization, -10.896957984833337, is the ground state at U = 4.64158883 and 3.03e-9 above the ground state at 4.64158882. Evidence: checks/hubbard-u-labels.
- lattice
- chain
- sites
- 14
- boundary
- periodic
- Nf
- 4
- U
- 4.64158883
- 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. The exact energy comes first where there is one; in every other group the lowest unflagged energy is its best value, and each row's distance is to that best (rules §6).
Numerically exact (1)
Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established. An exact energy is shown first, before the best of each other class. QMC is exact only within its error bar, which it must state, and reads exact (stochastic); an exact diagonalization outranks it. For a diagonalization resolved by symmetry sector only the ground state's sector is listed; the lowest energies of the other sectors are the instance's spectrum, in its JSON, and are not shown as the exact energy.
How these numbers were read
Where each number below was read, and how it was checked.
-0.7783541, ED
Checked 2026-09-16 · recomputed: Lanczos ED over the full fixed-(N_up, N_dn) space by two independent codes (checks/hubbard-u-labels/)
Reported as. -10.896957984833353 (ed_check.py) | -10.896957984834266 (ed_lib.mjs)
Reproduced at the grid U the instance now carries, not at the U of VarBench's name (relabels.mjs).
Coverage
Newest published number here: 2024. Literature last checked 2026-09-15 (table harvest of cached arXiv sources (match_tables.mjs --all), every matched paper read for this instance): 1 paper read, 0 of them with an energy on this page.