All instances / Electron gas, 2D
Electron gas, 2D square cell, N = 37, rs = 5, polarized
Record
-0.14373(4)
E/N (Ha)
Neural canonical transformation (normalizing-flow backflow on a plane-wave determinant)
10.21468/SciPostPhys.14.6.154 · lowest unflagged energy published, a strict variational bound
(rules §6)
The Hamiltonian
H = −½ ∑i ∇i2 + ∑i<j vE(ri − rj) + Nξ/2
Homogeneous electron gas in 2D: N↑ = 37, N↓ = 0 in a periodic square cell at rs = 5 bohr, Γ point. vE is the Ewald-summed Coulomb interaction with a uniform neutralizing background, ξ the Madelung term. Hartree atomic units; the energy per electron is E/N.
- cell
- square
- electrons
- 37
- boundary
- periodic
- N_up
- 37
- N_dn
- 0
- rs
- 5
- twist
- Gamma
- energies
- 1
Stored as a total energy in Hartree (rules §12); quoted here as
E/N (Ha), the energy per electron
(how the conversion works).
Every published energy
Grouped by what the number is. Where the instance is not solved, the lowest unflagged energy of any group is the record.
Strict variational upper bounds (1)
Where the instance is not solved, the record is the lowest unflagged energy in this group or among the projected and extrapolated ones, with or without an error bar; where it is solved, the exact energy is the record and the lowest of these is the closest challenger.
How these numbers were read
Where each number below was read, and how it was checked.
-0.14373(4) — Neural canonical transformation (normalizing-flow backflow...
Checked 2026-10-16 · source text of arXiv:2201.03156 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. −0.28746(8)
Fig. 2(b) caption (value read from caption text; the figure curve is not a table); sources/2201.03156.txt line 266; printed in Ry per electron; version read: arXiv text; SciPost copy not read | Rydberg ('We set the energy unit to be Rydberg'), converted × 1/2; N electrons in a two-dimensional periodic box of length L (square cell), spin polarized; QMBL's HF check: -0.14373 Ha per electron is 0.0118 Ha below QMBL's HF energy -0.1319137.
Coverage
Newest published number here: 2023.