The Hamiltonian
H = −½ ∑i ∇i2 + ∑i<j vE(ri − rj) + Nξ/2
Homogeneous electron gas in 3D: N↑ = 7, N↓ = 7 in a periodic sc cell at rs = 15 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
- sc
- electrons
- 14
- boundary
- periodic
- N_up
- 7
- N_dn
- 7
- rs
- 15
- twist
- Gamma
- energies
- 6
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.
-0.0408619(1) — FermiNet (16 determinants, Gaussian basis transformation)
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. -0.572067(2)
Table III (SM S3.D), rs=15, column E n_det=16; sources/2604.15888.txt line 1328; 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.
-0.0408578(1) — FermiNet (16 determinants)
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. -0.572009(2)
Table III (SM S3.D), rs=15, column E' n_det=16; sources/2604.15888.txt line 1328; 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.
-0.0408060(6) — FermiNet (4 determinants, Gaussian basis transformation)
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. -0.571284(9)
Table III (SM S3.D), rs=15, column E n_det=4; sources/2604.15888.txt line 1328; 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.
-0.040804(1) — FermiNet (1 determinant, Gaussian basis transformation)
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. -0.57125(2)
Table III (SM S3.D), rs=15, column E n_det=1; sources/2604.15888.txt line 1328; 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.
-0.0407969(6) — FermiNet (4 determinants)
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. -0.571157(8)
Table III (SM S3.D), rs=15, column E' n_det=4; sources/2604.15888.txt line 1328; 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.
-0.040774(4) — FermiNet (1 determinant)
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. -0.57083(5)
Table III (SM S3.D), rs=15, column E' n_det=1; sources/2604.15888.txt line 1328; 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.