We introduce the concept of fractured stochastic orbitals (FSOs), short vectors that sample a small number of space points and enable an efficient stochastic sampling of any general function. As a first demonstration, FSOs are applied in conjunction with simple direct-projection to accelerate our recent stochastic GW technique; the new developments enable accurate prediction of G0W0 quasiparticle energies and gaps for systems with up to Ne>10,000 electrons, with small statistical errors of ±0.05eV and using less than 2000 core CPU hours. Overall, stochastic GW scales now linearly (and often sub-linearly) with Ne.
@article{arxiv.1805.10554,
title = {Swift $GW$ beyond $10,000$ electrons using fractured stochastic orbitals},
author = {Vojtěch Vlček and Wenfei Li and Roi Baer and Eran Rabani and Daniel Neuhauser},
journal= {arXiv preprint arXiv:1805.10554},
year = {2018}
}