Post-GW theory and its application to pseudogap in strongly correlated system

The GW approximation is a widely used framework for studying correlated materials, but it struggles with certain limitations, such as its inability to explain pseudogap phenomena. To overcome these problems, we propose a systematic theoretical framework for Green's function corrections and apply it specifically to the GW approximation. In this new theory, the screened potential is reconnected to the physical response function, i.e. the covariant response function proposed in Phys. Rev. B 107, 085106 (2023), rather than using the RPA formula. We apply our scheme to calculate Green's function, the spectral function, and the charge compressibility in the two-dimensional Hubbard model. Our scheme yields significant qualitative and quantitative improvements over the standard GW method and successfully captures the pseudogap behavior.