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Hubbard rectangular 4x8, periodic/open, U = 8, n = 0.875

Hubbard/rectangular-4x8_32_PO_14_8

Record

-0.7363906 E/site

DMRG (MaxLinkDim = 12000, MaxTruncErr~6.6E-06, extrap energy -23.5658 +/- 0.0003)

run script, no paper cited · 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 = 14 on 32 sites.

lattice
rectangular-4x8
sites
32
boundary
periodic/open
Nf
14
U
8
energies
4

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 (4)

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

E/siteσVar(E)V-score methodsourceyear
-0.7363906record n/a 1.55e-2 8.2e-5 DMRG (MaxLinkDim = 12000, MaxTruncErr~6.6E-06, extrap energy -23.5658 +/- 0.0003)
VarBench reference run
run script, no paper cited n/a
-0.73500(3) 3.1e-5 3.50e-2 1.9e-4 VMC Hidden Fermion Determinant State Ansatz (N_hidden = 16. Single hidden layer fully connected net with alpha = 14). Soft mean-field constraint for lambda = 8 stripe order. Moreno et al. (2022) 2022
-0.73342(8) 8.0e-5 7.20e-1 3.8e-3 Hidden-fermion determinant state (HFDS), 8x4 cylinder
peer reviewed
Sharma et al. (2025) 2025
-0.7332(6) 6.0e-4 7.52e-1 4.0e-3 Jastrow-backflow (JBf), 8x4 cylinder
peer reviewed
Sharma et al. (2025) 2025

How these numbers were read

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

-0.73342(8) — Hidden-fermion determinant state (HFDS), 8x4 cylinder

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

Reported as. E_0/M = -0.73342 (+/- 0.00008), sigma^2/M = 0.0225

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 (8x4)".

-0.7332(6) — Jastrow-backflow (JBf), 8x4 cylinder

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

Reported as. E_0/M = -0.7332 (+/- 0.0006), sigma^2/M = 0.0235

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 (8x4)".

Coverage

Newest published number here: 2025. 2 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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