Record
-0.02272554(2)
E/N (Ha)
MP-NQS (2 message-passing iterations, plane-wave reference, Gaussian basis transformation)
arXiv:2604.15888 · 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 3D: N↑ = 18, N↓ = 18 in a periodic rect-3x3x2 cell at rs = 30 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
- rect-3x3x2
- electrons
- 36
- boundary
- periodic
- N_up
- 18
- N_dn
- 18
- rs
- 30
- twist
- Gamma
- energies
- 4
Stored as a total energy in Hartree (rules §12); quoted here as
E/N (Ha), the energy per electron
(how the conversion works).
How these numbers were read
Where each number below was read, and how it was checked.
-0.02272554(2) — MP-NQS (2 message-passing iterations, plane-wave reference...
Checked 2026-10-16 · source text of arXiv:2604.15888 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. -0.8181196(7)
Table IV (SM S3.D), rs=30, column E iteration=2; sources/2604.15888.txt line 1341; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.
-0.02272548(1) — MP-NQS (2 message-passing iterations, plane-wave reference)
Checked 2026-10-16 · source text of arXiv:2604.15888 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. -0.8181171(4)
Table IV (SM S3.D), rs=30, column E' iteration=2; sources/2604.15888.txt line 1341; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.
-0.02271169(8) — MP-NQS (1 message-passing iterations, plane-wave reference...
Checked 2026-10-16 · source text of arXiv:2604.15888 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. -0.817621(3)
Table IV (SM S3.D), rs=30, column E iteration=1; sources/2604.15888.txt line 1341; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.
-0.02271122(6) — MP-NQS (1 message-passing iterations, plane-wave reference)
Checked 2026-10-16 · source text of arXiv:2604.15888 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. -0.817604(2)
Table IV (SM S3.D), rs=30, column E' iteration=1; sources/2604.15888.txt line 1341; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.