Record
-0.0084646(1)
E/N (Ha)
Fixed-node DMC (trial state: Slater-Jastrow, ferromagnetic bcc crystal; extrapolated: Δτ → 0)
10.1103/PhysRevB.105.245135 · lowest unflagged energy published, a projected estimate
(rules §6)
The Hamiltonian
H = −½ ∑i ∇i2 + ∑i<j vE(ri − rj) + Nξ/2
Homogeneous electron gas in 3D: N↑ = 216, N↓ = 0 in a periodic bcc cell at rs = 90 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
- bcc
- electrons
- 216
- boundary
- periodic
- N_up
- 216
- N_dn
- 0
- rs
- 90
- twist
- Gamma
- energies
- 2
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. On a solved instance the exact energy is the record; otherwise the lowest unflagged energy of any group holds it (rules §6).
Strict variational upper bounds (1)
Energies that a variational state reached (VMC, DMRG and MPS at finite bond dimension, PEPS, NQS, VQE). Each is an upper bound on the ground-state energy.
Projected or fixed-node estimates (1)
Variational only within a constraint: fixed-node, constrained-path, GFMC on a trial state. Each depends on its node or constraint, so two of them are not cleanly comparable to each other or to strict bounds.
How these numbers were read
Where each number below was read, and how it was checked.
-0.0084646(1), Fixed-node DMC (trial state: Slater-Jastrow, ferromagnetic...
Checked 2026-10-20 · source text of arXiv:2201.08743 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. −0.0084646(1)
SM Table IX, N = 216, row E_DMC, column rs = 90; SupplMat.pdf (PRB 105, 245135), pypdf layout text line 299; printed in Ha per electron | bcc simulation cell of N = n^3 electrons holding a bcc Wigner crystal; crystal energies are not twist-averaged and the twist has no observable effect (main text); the same convention as the main-text crystal rows (Tables I and II), which QMBL carries.
-0.00843484(6), Slater-Jastrow (ferromagnetic bcc crystal)
Checked 2026-10-20 · source text of arXiv:2201.08743 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. −0.00843484(6)
SM Table IX, N = 216, row E_VMC, column rs = 90; SupplMat.pdf (PRB 105, 245135), pypdf layout text line 297; printed in Ha per electron | bcc simulation cell of N = n^3 electrons holding a bcc Wigner crystal; crystal energies are not twist-averaged and the twist has no observable effect (main text); the same convention as the main-text crystal rows (Tables I and II), which QMBL carries. | variance reported as 0.00001779(8), not stored: convention not verified