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Since the earliest implementations of the various GW approximations andcumulant expansion in the calculations of quasiparticle propagators andspectra, several attempts have been made to combine the advantageous propertiesand results of these two theoretical approaches. While the GW plus cumulantapproach has proven successful in interpreting photoemission spectroscopy datain solids, the formal connection between the two methods has not beeninvestigated in detail. By introducing a general bijective integralrepresentation of the cumulants, we can rigorously identify at which pointthese two approximations can be connected for the paradigmatic model ofquasiparticle interaction with the dielectric response of the system that hasbeen extensively exploited in recent interpretations of the satellitestructures in photoelectron spectra. We establish a protocol for consistentpractical implementation of the thus established GW+cumulant scheme, andillustrate it by comprehensive state-of-the-art first-principles calculationsof intrinsic angle-resolved photoemission spectra from Si valence bands.

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands