  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 large complex assemblies due to its large 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 ($\gtrapprox$ 10 atoms) and 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.
