Hubbard square 8x8, U = 8, n ≈ 0.7813

Hubbard/square_64_P_25_8

Record

-0.91483(2) E/site

mVMC with SU(2) and momentum projections (gamma point) + RBM + Lanczos, (U=8), alpha = 8 with 1x1 RBM subspace

run script, no paper cited · 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_↓ = 25 on 64 sites.

lattice: square
sites: 64
boundary: periodic
Nf: 25
U: 8
energies: 3

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 (2)

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

E/site	σ	Var(E)	V-score	method	source	year
-0.91483(2)record	1.6e-5	2.58e+0	6.9e-3	mVMC with SU(2) and momentum projections (gamma point) + RBM + Lanczos, (U=8), alpha = 8 with 1x1 RBM subspace VarBench reference run	run script, no paper cited	n/a
-0.91012(2)	2.2e-5	3.46e+0	9.3e-3	VMC with uniform BCS pairing (+Jastrow and backflow) VarBench reference run	run script, no paper cited	n/a

Projected or fixed-node estimates (1)

Variational only within a constraint: fixed-node, constrained-path, GFMC on a trial state. Node- or constraint-dependent, so not cleanly comparable to each other or to the group above, and never the record.

E/site	σ	Var(E)	V-score	method	source	year
-0.913753(9)	9.4e-6	n/a	n/a	FN on the state above VarBench reference run	run script, no paper cited	n/a

Coverage

No row here carries a publication year. Nothing has been added to this instance since the VarBench snapshot of 2024-10-22.

This instance as data

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