All instances / Hubbard
Hubbard square 8x8, U = 4, n = 0.875
Best values
(rules §6)
| best variational |
-1.01391(8) |
VAFQMC |
| best projected |
-1.01923(6) |
CP-AFQMCLevy et al. (2023) · the lowest unflagged projected energy, a projected estimate, which depends on its node or constraint |
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, N↑ = N↓ = 28 on 64 sites.
- lattice
- square
- sites
- 64
- boundary
- periodic
- Nf
- 28
- U
- 4
- energies
- 4
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 (2)
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.
Projected or fixed-node estimates (2)
Variational only within a constraint: fixed-node, constrained-path, GFMC on a trial state. Each depends on its node or constraint, so two of them are not cleanly comparable to each other or to strict bounds.
How these numbers were read
Where each number below was read, and how it was checked.
-1.01923(6), CP-AFQMC
Checked 2026-09-15 · source text of arXiv:2308.08594 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. −1.01923(6)
Table I | 8x8=64 sites P; n=0.875 filling => Nf=28 per spin; U=4; catalogue best_per_site for this instance is -1.0086406, so this quoted value is notably lower (stronger) than the current catalogue best
-1.01391(8), VAFQMC
Checked 2026-09-15 · source text of arXiv:2308.08594 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. −1.01391(8)
Table I | same instance as above; also lower than the current catalogue best_per_site -1.0086406 | variance reported as 0.6, not stored: convention not verified
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): 8 papers read, 0 of them with an energy on this page.