Most currently used approximations for the one-particle Green's function G in the framework of many-body perturbation theory, such as Hedin's GW approximation or the cumulant GW+C approach, are based on a linear response approximation for the screened interaction W. The extent to which such a hypothesis is valid and ways to go beyond have been explored only very little. Here we show how to derive a cumulant Green's function beyond linear-response from the equation of motion of the Green's function in a functional derivative formulation. The results can be written in a compact form, which opens the possibility to calculate the corrections in a first principles framework using time-dependent density functional theory. In order to illustrate the potential importance of the corrections, numerical results are presented for a model system with a core level and two valence orbitals.
Expansion of Momentum Space and Full 2$π$ Solid Angle Photoelectron Collection in Laser-Based Angle-Resolved Photoemission Spectroscopy by Applying Sample Bias
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Technical Institute of Physics and Chemistry, Chinese Academy of Sciences（中国科学院化学物理研究所）；Songshan Lake Materials Laboratory（松山湖材料实验室）
