Hubbard square 4x4, U = 6, n = 1

Hubbard/square_16_P_8_6

No record

—

solved exactly (rules §6). Every row is still listed below.

The Hamiltonian

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

t = 1, U = 6, N_↑ = N_↓ = 8 on 16 sites.

lattice: square
sites: 16
boundary: periodic
Nf: 8
U: 6
energies: 1

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.

Numerically exact (1)

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
-0.6588(3)	2.5e-4	n/a	n/a	AFQMC, sign-problem-free at half filling (tau = 0.01, Trotter error below the statistical error) peer reviewed	Qin, Shi & Zhang, Benchmark stud	n/a

How these numbers were read

Rows added after the VarBench import record where the number came from.

-0.6588(3) — AFQMC, sign-problem-free at half filling (tau = 0.01...

Checked 2026-09-15 · arXiv PDF extracted locally with pypdf in layout mode, E rows of Table IV parsed by column position; no LLM transcription

Reported as. E = -10.541(4) (total), 4 x 4, U = 6, PBC

Table IV, "Total ground state energy (E) ... in the Hubbard model at half-filling, for U = 2, 4, 6, 8 ... for both PBC and PBC-APBC. Statistical errors are on the last digit." Row 4 x 4, column U = 6 PBC. Half filling: N_up = N_dn = 8. Cross-checks: the 8 x 8 PBC values at U = 4 and 8 agree with VarBench's own AFQMC exact rows to 1.3 sigma, and the 8 x 8, 10 x 10 and 12 x 12 PBC U = 8 values with the AFQMC references quoted by arXiv:2507.02644 (Table S1) to the printed digits.

Coverage

No row here carries a publication year. 1 row added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

JSON · source file on GitHub · open an issue about this instance