Record
-0.7097(1)
E/site
Tensor backflow (wave function of the PBC run with pinning field PF3, re-optimised 1324 steps with open boundaries, 1 Lanczos step)
Liang (2026) · lowest unflagged energy published, a strict variational bound
(rules §6)
The Hamiltonian
H = −t1 ∑⟨ij⟩,σ (c†iσcjσ + h.c.) −t2 ∑⟨⟨ij⟩⟩,σ (c†iσcjσ + h.c.) + U ∑i ni↑ni↓
t1 = 1, t2 = -0.2, U = 8, N↑ = N↓ = 112 on 256 sites.
This instance is a t12 variant with a next-nearest-neighbour hopping t2, written as in VarBench's Eq. (S6). t2 is the t′ of the sources' H = −t ∑⟨ij⟩ − t′ ∑⟨⟨ij⟩⟩ + U ∑ ni↑ni↓. The couplings are those each source prints (see the rows).
- lattice
- square
- sites
- 256
- boundary
- open
- Nf
- 112
- U
- 8
- t1
- 1
- t2
- -0.2
- energies
- 2
Stored as a total energy; quoted here as
E/site, which is what the papers report
(how the conversion works).
How these numbers were read
Where each number below was read, and how it was checked.
-0.7097(1), Tensor backflow (wave function of the PBC run with pinning...
Checked 2026-10-22 · source text of arXiv:2609.22618 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -0.7097(1)
Section III.C (OBC) text; also Fig. 7 caption; sources/2609.22618.txt line 573; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_<ij> - t' sum_<<ij>> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.
-0.7048(7), Tensor backflow (wave function of the PBC run with pinning...
Checked 2026-10-22 · source text of arXiv:2609.22618 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. -0.7048(7)
Section III.C (OBC) text; sources/2609.22618.txt line 573; version read: arXiv v1 (sources/2609.22618.txt); no journal version (Crossref, arXiv abs page) | Eq. (8): H = -t sum_<ij> - t' sum_<<ij>> + U sum n_up n_dn, t = 1, t' = -0.2 (Eq. (S6) form of QMBL's t12 instances, t2 = t'), U = 8, n = 0.875, periodic; energies per site. The 16x16 pinning fields (Eq. 15) act during optimisation only and are removed before the Table III energies are measured.