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

Since the earliest implementations of the various GW approximations and cumulant expansion in the calculations of quasiparticle propagators and spectra, several attempts have been made to combine the advantageous properties and results of these two theoretical approaches. While the GW plus cumulant approach has proven successful in interpreting photoemission spectroscopy data in solids, the formal connection between the two methods has not been investigated in detail. By introducing a general bijective integral representation of the cumulants, we can rigorously identify at which point these two approximations can be connected for the paradigmatic model of quasiparticle interaction with the dielectric response of the system that has been extensively exploited in recent interpretations of the satellite structures in photoelectron spectra. We establish a protocol for consistent practical implementation of the thus established GW+cumulant scheme, and illustrate it by comprehensive state-of-the-art first-principles calculations of intrinsic angle-resolved photoemission spectra from Si valence bands.