Hubbard square 8x8, periodic/open, U = 8, n = 1

Hubbard/square_64_PO_32_8

Record

-0.49944(4) E/site

VAFQMC

Sorella (2023) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = −t ∑_⟨ij⟩,σ (c^†_iσc_jσ + h.c.) + U ∑_i n_i↑n_i↓

t = 1, U = 8, N_↑ = N_↓ = 32 on 64 sites.

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).

Grouped by what the number is. Ranking happens only inside the first group.

The record is the lowest eligible energy in this group, and only this group.

E/site	σ	Var(E)	V-score	method	source	year
-0.49944(4)record	3.6e-5	3.00e-2	7.5e-5	VAFQMC	Sorella (2023)	2023
-0.4984344	n/a	1.11e+0	2.8e-3	DMRG (MaxLinkDim=10000, MaxTruncErr ~ 3.4E-5, Extrap Energy -32.0027 +/- 0.0206) VarBench reference run	run script, no paper cited	n/a

Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established: the answer, not a claim about it.

E/site	σ	Var(E)	V-score	method	source	year
-0.5005(2)	2.3e-4	n/a	n/a	AFQMC (Metropolis, Trotter error extrapolated), numerically exact	Shi et al. (2015)	2015

Newest published number here: 2023. Nothing has been added to this instance since the VarBench snapshot of 2024-10-22.