Real-time cumulant Green’s function including non-linear corrections

The cumulant approximation to the one electron Green's function has recently gained attention as an improved method for including the effects of many-body excitations in calculations of x-ray spectra [1]. Multiple plasmon satellites in the XPS spectra of solid-state systems are well reproduced by the cumulant, but not the GW approximation. Approximations of the cumulant are usually based on an expansion to linear order in the screened coulomb interaction, but this may become inadequate at higher correlation. Recently, a new approach for including non-linear contributions was presented, and a simple approximation was proposed based on real-time TDDFT [2]. Here we apply this new approximation and compare to the linear response form as well as to available experimental data. Extensions of the approximation are also briefly discussed.

[1] Jianqiang Sky Zhou et al., J. Chem. Phys. 143, 194109 (2015).
[2] M. Tzavala et al., Phys. Rev. Research 2, 033147 (2020).