Record
-0.03199636(7)
E/N (Ha)
Fixed-phase DMC (trial state: Fermi Sets, 5.0e4 parameters)
arXiv:2607.25872 · 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 2D: N↑ = 16, N↓ = 0 in a periodic triangular 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
- triangular
- electrons
- 16
- boundary
- periodic
- N_up
- 16
- N_dn
- 0
- rs
- 30
- 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).
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 (3)
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.
Projected or fixed-node estimates (3)
Variational only within a constraint: fixed-node, constrained-path, GFMC on a trial state. Node- or constraint-dependent, so not cleanly comparable to each other or to strict bounds. Like any unflagged energy, one holds the record where it is the lowest on an unsolved instance.
How these numbers were read
Where each number below was read, and how it was checked.
-0.03199636(7) — Fixed-phase DMC (trial state: Fermi Sets, 5.0e4 parameters)
Checked 2026-10-16 · source text of arXiv:2607.25872 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. −0.03199636(7)
Table III, N_p=5.0 x 10^4, column E_DMC; sources/2607.25872.txt line 367; printed in Ha per electron; version read: arXiv text with its appendices; journal version not checked (arXiv lookup timed out; none on Crossref) | Ha per electron (Table III caption), hexagonal (triangular) cell; Appendix E: the constant in H is the Madelung energy of the cell. QMBL's HF check: the fixed-phase DMC energies sit 0.0043 Ha per electron below QMBL's HF energy -0.0276351 (an open shell at N = 16).
-0.031990687(3) — Fermi Sets (4 determinants, 5.0e4 parameters)
Checked 2026-10-16 · source text of arXiv:2607.25872 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. −0.031990687(3)
Table III, N_p=5.0 x 10^4, column E_VMC; sources/2607.25872.txt line 367; printed in Ha per electron; version read: arXiv text with its appendices; journal version not checked (arXiv lookup timed out; none on Crossref) | Ha per electron (Table III caption), hexagonal (triangular) cell; Appendix E: the constant in H is the Madelung energy of the cell. QMBL's HF check: the fixed-phase DMC energies sit 0.0043 Ha per electron below QMBL's HF energy -0.0276351 (an open shell at N = 16).
-0.03197786(8) — Fixed-phase DMC (trial state: Fermi Sets, 3.7e4 parameters)
Checked 2026-10-16 · source text of arXiv:2607.25872 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. −0.03197786(8)
Table III, N_p=3.7 x 10^4, column E_DMC; sources/2607.25872.txt line 366; printed in Ha per electron; version read: arXiv text with its appendices; journal version not checked (arXiv lookup timed out; none on Crossref) | Ha per electron (Table III caption), hexagonal (triangular) cell; Appendix E: the constant in H is the Madelung energy of the cell. QMBL's HF check: the fixed-phase DMC energies sit 0.0043 Ha per electron below QMBL's HF energy -0.0276351 (an open shell at N = 16).
-0.031965678(6) — Fermi Sets (4 determinants, 3.7e4 parameters)
Checked 2026-10-16 · source text of arXiv:2607.25872 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. −0.031965678(6)
Table III, N_p=3.7 x 10^4, column E_VMC; sources/2607.25872.txt line 366; printed in Ha per electron; version read: arXiv text with its appendices; journal version not checked (arXiv lookup timed out; none on Crossref) | Ha per electron (Table III caption), hexagonal (triangular) cell; Appendix E: the constant in H is the Madelung energy of the cell. QMBL's HF check: the fixed-phase DMC energies sit 0.0043 Ha per electron below QMBL's HF energy -0.0276351 (an open shell at N = 16).
-0.0319114(1) — Fixed-phase DMC (trial state: Fermi Sets, 2.5e4 parameters)
Checked 2026-10-16 · source text of arXiv:2607.25872 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. −0.03191139(12)
Table III, N_p=2.5 x 10^4, column E_DMC; sources/2607.25872.txt line 365; printed in Ha per electron; version read: arXiv text with its appendices; journal version not checked (arXiv lookup timed out; none on Crossref) | Ha per electron (Table III caption), hexagonal (triangular) cell; Appendix E: the constant in H is the Madelung energy of the cell. QMBL's HF check: the fixed-phase DMC energies sit 0.0043 Ha per electron below QMBL's HF energy -0.0276351 (an open shell at N = 16).
-0.03189509(1) — Fermi Sets (4 determinants, 2.5e4 parameters)
Checked 2026-10-16 · source text of arXiv:2607.25872 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. −0.031895091(12)
Table III, N_p=2.5 x 10^4, column E_VMC; sources/2607.25872.txt line 365; printed in Ha per electron; version read: arXiv text with its appendices; journal version not checked (arXiv lookup timed out; none on Crossref) | Ha per electron (Table III caption), hexagonal (triangular) cell; Appendix E: the constant in H is the Madelung energy of the cell. QMBL's HF check: the fixed-phase DMC energies sit 0.0043 Ha per electron below QMBL's HF energy -0.0276351 (an open shell at N = 16).