  Electronic structure calculations based on many-body perturbation theory
(e.g. GW or the random-phase approximation (RPA)) require function evaluations
in the complex time and frequency domain, for example inhomogeneous Fourier
transforms or analytic continuation from the imaginary axis to the real axis.
For inhomogeneous Fourier transforms, the time-frequency component of the
GreenX library provides time-frequency grids that can be utilized in
low-scaling RPA and GW implementations. In addition, the adoption of the
compact frequency grids provided by our library also reduces the computational
overhead in RPA implementations with conventional scaling. In this work, we
present low-scaling GW and conventional RPA benchmark calculations using the
GreenX grids with different codes (FHI-aims, CP2K and ABINIT) for molecules,
two-dimensional materials and solids. Very small integration errors are
observed when using 30 time-frequency points for our test cases, namely
$<10^{-8}$ eV/electron for the RPA correlation energies, and 10 meV for the GW
quasiparticle energies.
