All instances / Hubbard
Hubbard square 16x16, U = 8, n ≈ 0.8828
Best values
(rules §6)
| best variational |
-0.74455(3) |
VAFQMCWu et al. (2024) · the lowest unflagged variational energy, a strict variational bound |
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 = 8, N↑ = N↓ = 113 on 256 sites.
- lattice
- square
- sites
- 256
- boundary
- periodic
- Nf
- 113
- U
- 8
- 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).
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.
Coverage
Newest published number here: 2024. Literature last checked 2026-09-15 (citation screen of Sorella 2023 (PRB 107, 115133), VAFQMC doping scan: citing works from OpenAlex and Semantic Scholar (scripts/cited_by.mjs)): 8 papers read, 0 of them with an energy on this page.