Complex-time shredded propagator method for large-scale GW calculations

The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to study large complex assemblies due to the method's high computational overhead and quartic scaling with particle number. Here, the GW equations are recast, exactly, as Fourier-Laplace time integrals over complex time propagators. The propagators are then "shredded" via energy partitioning and the time integrals approximated in a controlled manner using generalized Gaussian quadrature(s) while discrete variable methods are employed to represent the required propagators in real space. The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems (≳10 atoms) and offers 2-3 order of magnitude improvement in large systems (≈200-300 atoms). It also represents a substantial improvement over other cubic methods tested for all system sizes studied. The approach can be applied to any theoretical framework containing large sums of terms with energy differences in the denominator.