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Hubbard square 8x8, U = 8, n = 0.875

Hubbard/square_64_P_28_8

Record

-0.7458(6) E/site

Jastrow-backflow (JBf), 8x8 torus

Sharma et al. (2025) · lowest eligible strict variational bound (rules §6)

The Hamiltonian

H = −t ∑⟨ij⟩,σ (cc + h.c.) + U ∑i ni↑ni↓

t = 1, U = 8, N = N = 28 on 64 sites.

lattice
square
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).

Every published energy

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

Strict variational upper bounds (7)

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

E/siteσVar(E)V-score methodsourceyear
-0.7458(6)record 6.0e-4 3.36e+0 8.9e-3 Jastrow-backflow (JBf), 8x8 torus
peer reviewed
Sharma et al. (2025) 2025
-0.7454(9) 9.0e-4 3.60e+0 9.5e-3 Hidden-fermion determinant state (HFDS), 8x8 torus
peer reviewed
Sharma et al. (2025) 2025
-0.74220(3) 3.1e-5 6.62e+0 1.8e-2 VMC with uniform BCS pairing (+Jastrow and backflow)
VarBench reference run
run script, no paper cited n/a
-0.7422(3) 3.0e-4 4.47e+0 1.2e-2 JBf-ViT (vision transformer backflow), 8x8 torus
peer reviewed
Sharma et al. (2025) 2025
-0.736(1) 1.0e-3 6.72e+0 1.8e-2 HFDS-ViT, 8x8 torus
peer reviewed
Sharma et al. (2025) 2025
-0.729(4) 4.0e-3 8.90e+0 2.4e-2 HFDS Symm-ViT-Ti, 8x8 torus
peer reviewed
Sharma et al. (2025) 2025
-0.726(9) 9.0e-3 1.08e+1 2.9e-2 JBf Symm-ViT-Ti, 8x8 torus
peer reviewed
Sharma et al. (2025) 2025

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/siteσVar(E)V-score methodsourceyear
-0.74928(2) 1.6e-5 n/a n/a FN on the state above
VarBench reference run
run script, no paper cited n/a

How these numbers were read

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

-0.7458(6) — Jastrow-backflow (JBf), 8x8 torus

Checked 2026-09-14 · arXiv HTML parsed locally, no LLM transcription

Reported as. E_0/M = -0.7458 (+/- 0.0006), sigma^2/M = 0.0525

Read from Table 1 of arXiv:2510.11710 (U/t = 8, n_h = 1/8, energies per site, 131072 samples), parsed from the arXiv HTML. Row "JBf (8x8 Torus)".

-0.7454(9) — Hidden-fermion determinant state (HFDS), 8x8 torus

Checked 2026-09-14 · arXiv HTML parsed locally, no LLM transcription

Reported as. E_0/M = -0.7454 (+/- 0.0009), sigma^2/M = 0.0563

Read from Table 1 of arXiv:2510.11710 (U/t = 8, n_h = 1/8, energies per site, 131072 samples), parsed from the arXiv HTML. Row "HFDS (8x8 Torus)".

-0.7422(3) — JBf-ViT (vision transformer backflow), 8x8 torus

Checked 2026-09-14 · arXiv HTML parsed locally, no LLM transcription

Reported as. E_0/M = -0.7422 (+/- 0.0003), sigma^2/M = 0.0698

Read from Table 1 of arXiv:2510.11710 (U/t = 8, n_h = 1/8, energies per site, 131072 samples), parsed from the arXiv HTML. Right-hand table, row "JBf-ViT"; same lattice and parameters per the caption.

-0.736(1) — HFDS-ViT, 8x8 torus

Checked 2026-09-14 · arXiv HTML parsed locally, no LLM transcription

Reported as. E_0/M = -0.736 (+/- 0.001), sigma^2/M = 0.105

Read from Table 1 of arXiv:2510.11710 (U/t = 8, n_h = 1/8, energies per site, 131072 samples), parsed from the arXiv HTML. Right-hand table, row "HFDS-ViT".

-0.729(4) — HFDS Symm-ViT-Ti, 8x8 torus

Checked 2026-09-14 · arXiv HTML parsed locally, no LLM transcription

Reported as. E_0/M = -0.729 (+/- 0.004), sigma^2/M = 0.139

Read from Table 1 of arXiv:2510.11710 (U/t = 8, n_h = 1/8, energies per site, 131072 samples), parsed from the arXiv HTML. Right-hand table, row "HFDS Symm-ViT-Ti".

-0.726(9) — JBf Symm-ViT-Ti, 8x8 torus

Checked 2026-09-14 · arXiv HTML parsed locally, no LLM transcription

Reported as. E_0/M = -0.726 (+/- 0.009), sigma^2/M = 0.168

Read from Table 1 of arXiv:2510.11710 (U/t = 8, n_h = 1/8, energies per site, 131072 samples), parsed from the arXiv HTML. Right-hand table, row "JBf Symm-ViT-Ti".

Coverage

Newest published number here: 2025. 6 rows added from the 2026-09 literature sweep, on top of the VarBench snapshot of 2024-10-22.

This instance as data

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