The Hamiltonian
H = −t ∑⟨ij⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓
t = 1, U = 8, N↑ = N↓ = 14 on 32 sites.
- lattice
- rectangular-4x8
- sites
- 32
- boundary
- periodic
- Nf
- 14
- 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).
How these numbers were read
Rows added after the VarBench import record where the number came from.
-0.76690(1) — HFPS (hidden-fermion Pfaffian state)
Checked 2026-09-15 · arXiv PDF text extracted locally with pypdf in layout mode, no LLM transcription
Reported as. -0.76690(1) per site, sigma^2/N_site = 0.016320
Table IV of arXiv:2507.10705, "Raw data of Fig. 7 in the L x 4 lattice with 1/8 doping and U = 8", row 8 x 4; Sec. III states Fig. 7 shows "L x 4 PBC lattices". 32 sites, 28 electrons, U = 8, periodic: this instance. The same table's 16 x 4 value -0.76413(3) is the HFPS row on rectangular-4x16_64_P_28_8, and its 4 x 4 value -0.74177(5) sits 3e-5 above the ED energy -0.7418 quoted by arXiv:2606.00924. New record, 0.47% below the VarBench HFDS row -0.7633125 and below the RHB -0.7641(3) of arXiv:2606.00924 on the same lattice. Variance: sigma^2/N_site stored as a total (x 32). Its V-score, 2.7e-3, is ~25x the VarBench HFDS row's 1.1e-4 at a higher energy; the HFDS variance is the likelier outlier, since on 4x16 the same VarBench ansatz has ten times the per-site variance and this paper puts HFDS 3e-4 above exact already at 4x4. Read from the arXiv version; the PNAS version was not compared (pnas.org refuses this sandbox).
-0.7641(3) — RHB (hierarchical backflow K = 2 + nonlocal FNN factor...
Checked 2026-09-15 · arXiv PDF text extracted locally with pypdf in layout mode, no LLM transcription
Reported as. -0.7641 per site, table-wide sampling error ~0.0003
Table IV of arXiv:2606.00924, "Energies per site for the Hubbard model at nh = 0.125, U = 8 for different systems under periodic boundary conditions. The energy sampling errors are around 0.0003", row 4 x 8, column RHB (Ndet = 5, Nneuron = 100, the setting adopted for all large-scale runs after Table III). Instance identity: the same row's HFDS column, -0.7633, is the VarBench HFDS row -0.7633125. sigma is the caption's table-wide "around 0.0003". Layout mode shifts this row one column left in sweep-tables.tsv; read here from the printed table. Internal check: the same ansatz gives -0.7410 on 4 x 4 against ED -0.7418 (Table III), above exact as it must be.