Good-Γ Numbers: A Shell-Optimized Route to the Thermodynamic Limit in Quantum Monte Carlo Calculations of the High-Density Two-Dimensional Electron Gas
Abstract
Single-particle finite-size errors remain a central obstacle in quantum Monte Carlo (QMC) simulations of periodic systems, conventionally reduced via twist averaging (TA). Here we introduce Good-Γ (GG) particle numbers as system sizes N at which the Γ-point Hartree--Fock (HF) energy of the high-density two-dimensional uniform electron gas (2D UEG) lies anomalously close to its thermodynamic-limit (TL) value. All results in this work concern the 2D UEG in its high-density Fermi-liquid regime, rs=1--$4$. We systematically investigate the kinetic- and exchange-energy errors, ΔKE(N) and ΔEX(N), that underlie this one-body finite-size-error cancellation across four densities and both spin polarizations. We then compare diffusion Monte Carlo (DMC) energies extrapolated to the TL from GG-N sequences against twist-averaged extrapolations at the same densities and polarizations, finding agreement to within a fraction of a millihartree in every case, independent of whether a 1/N or an N−5/4 extrapolation form is used.
Related
- A dipole-forbidden conduction-band transition and the mid-infrared absorption of n-type Mg2Si, Mg2Ge and Mg2Sn: all-electron quasiparticle self-consistent GW calculations
- First-principles calculations of the thermodynamic factor of multicomponent alloys
- Atomic structure calculations for constraining new electron-electron forces
- An efficient approach to electron-phonon coupling calculations of heterostructures within an all-electron framework
- Origin of the Difference between Kohn-Sham and ∆SCF Band gaps for Delocalized Electron–Hole Excitations in Hybrid-Functional Supercell Calculations
BibTeX
@misc{azadi2026goodγ,
title = {{Good-$Γ$ Numbers: A Shell-Optimized Route to the Thermodynamic Limit in Quantum Monte Carlo Calculations of the High-Density Two-Dimensional Electron Gas}},
author = {S. Azadi and T. D. Kühne and A. Principi and M. S. Bahramy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27761},
eprint = {2610.27761},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27761},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Good-Γ Numbers: A Shell-Optimized Route to the Thermodynamic Limit in Quantum Monte Carlo Calculations of the High-Density Two-Dimensional Electron Gas
AU - S. Azadi
AU - T. D. Kühne
AU - A. Principi
AU - M. S. Bahramy
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27761
UR - https://arxiv.org/abs/2610.27761
AB - Single-particle finite-size errors remain a central obstacle in quantum Monte Carlo (QMC) simulations of periodic systems, conventionally reduced via twist averaging (TA). Here we introduce Good-Γ (GG) particle numbers as system sizes N at which the Γ-point Hartree--Fock (HF) energy of the high-density two-dimensional uniform electron gas (2D UEG) lies anomalously close to its thermodynamic-limit (TL) value. All results in this work concern the 2D UEG in its high-density Fermi-liquid regime, r_s=1--$4$. We systematically investigate the kinetic- and exchange-energy errors, ΔKE(N) and ΔEX(N), that underlie this one-body finite-size-error cancellation across four densities and both spin polarizations. We then compare diffusion Monte Carlo (DMC) energies extrapolated to the TL from GG-N sequences against twist-averaged extrapolations at the same densities and polarizations, finding agreement to within a fraction of a millihartree in every case, independent of whether a 1/N or an N^−5/4 extrapolation form is used.
ER -