The Hamiltonian
H = −t ∑⟨ij⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓
t = 1, U = 7.74263683, N↑ = N↓ = 5 on 16 sites.
Upstream this instance is Hubbard/square_16_P_5_7.74264. The name's 7.74264 rounds the coupling of this Hamiltonian, 7.74263683 (10^(8/9)). The exact diagonalization, -17.60373155517909, is the ground state there; at U = 7.74264 the ground state is 1.18e-6 higher, so the stored exact energy sat below the ground state of the instance as named. Evidence: checks/hubbard-u-labels.
- lattice
- square
- sites
- 16
- boundary
- periodic
- Nf
- 5
- U
- 7.74263683
- energies
- 2
Stored as a total energy in the convention of
VarBench; quoted here as
E/site, which is what the papers report
(how the conversion works).
Every published energy
Grouped by what the number is. Ranking happens only inside the first group.
Strict variational upper bounds (1)
Where the instance is not solved, the record is the lowest eligible energy in this group; where it is, the lowest eligible energy here is the best variational bound and the closest challenger to the exact one.
Numerically exact (1)
Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established: the answer, not a claim about it, and therefore the record wherever one exists. QMC is exact only within its statistical error bar, which it must state, and its rows read exact (stochastic); an exact diagonalization outranks it. Sector-resolved diagonalizations state the lowest energy in one symmetry sector and do not hold it.