The Hamiltonian
H = −t ∑⟨ij⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓
t = 1, U = 8, N↑ = N↓ = 28 on 64 sites.
- lattice
- rectangular-4x16
- sites
- 64
- boundary
- periodic
- Nf
- 28
- U
- 8
- energies
- 8
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).
How these numbers were read
Rows added after the VarBench import record where the number came from.
-0.76647(2) — ACE (16 conv layers) trial state + fixed-node GFMC
Checked 2026-09-10 · source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription
Reported as. -0.76647 (+/- 0.00002) per site
Sec. III.3.1: "a GFMC calculation with the ACE trial wave-function gives an even lower energy of -0.76647(2)". Fixed-node: upper bound but node-dependent.
-0.76623(1) — ACE (16 conv layers) + full symmetry projection
Checked 2026-09-10 · source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription
Reported as. -0.76623 (+/- 0.00001) per site
Sec. III.3.1: "reach a new state-of-the-art energy of -0.76623(1)".
-0.76560(1) — NNBF, 32 determinants + free projection to the fully...
Checked 2026-09-10 · source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription
Reported as. -0.7656 (+/- 0.00001) per site
Sec. III: "further projected at essentially no cost to the fully symmetric state to reach an energy of -0.76560(1)". This is the best 4x16 number in arXiv:2510.26906v1.
-0.76486(2) — NNBF, symmetry optimization with 32 determinants
Checked 2026-09-10 · source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription
Reported as. -0.76486 (+/- 0.00002) per site
Same section, before the free projection.
-0.76464(1) — ACE (16 conv layers), no explicit symmetry
Checked 2026-09-10 · source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription
Reported as. -0.76464 (+/- 0.00001) per site
Sec. III.3.1: "achieves a ground-state energy of -0.76464(1)".
-0.76413(3) — HFPS (hidden-fermion Pfaffian state)
Checked 2026-09-13 · arXiv HTML parsed locally, no LLM transcription
Reported as. -0.76413 (+/- 0.00003) per site
Sec. III: "The energy we obtain in the 16x4 lattice is E/N = -0.76413, outperforming a recent result E/N = -0.76298 produced by Transformer-NNBF". Instance identity confirmed by that comparison value; the number is independently quoted as the HFPS result by both arXiv:2604.25775 and arXiv:2510.26906. No error bar in Sec. III; Table IV of the same paper (raw data of Fig. 7, L x 4 PBC lattices, 1/8 doping, U = 8) gives -0.76413(3) and sigma^2/N_site = 0.031283, added 2026-09-15. Published as PNAS 123, e2535288123 (2026); read from the arXiv version, the journal version not compared.
-0.7629800 ○ — Transformer backflow + MARCH optimizer
Checked 2026-09-10 · source text/table parsed locally (arXiv HTML or pypdf), no LLM transcription
Reported as. -0.76298 per site
Supp. Sec. 4.1: "our NQS yields a ground state energy of -0.76298" on 16x4 PBC. Instance identity confirmed: same passage quotes HFDS -0.753(2), matching the VarBench row -0.753000(47). No error bar given.