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 $G_{ 0}W_{ 0}$ quasiparticle energies and gaps for systems with up to $N_{ e}>10,000$ electrons, with small statistical errors of $\pm0.05\,{ \rm eV}$ and using less than 2000 core CPU hours. Overall, stochastic $GW$ scales now linearly (and often sub-linearly) with $N_{ e}.$
Categories: physics.comp-ph