Zero-Point renormalization of the band structure within Quasiparticle Self-consistent GW

The reliability of Density Functional Theory (DFT) for the electron-phonon coupling in many materials, including even simple sp-bonded compounds, has been questioned in recent years. Hybrid functionals and quasiparticle GW corrections suggest that nonlocal exchange-correlation enhances the electron-phonon interaction as a consequence of an improved description of the electronic screening. This has highlighted the need to move beyond local exchange-correlation functionals within DFT, but complete field-theoretic investigations are still missing in literature. In this talk I will introduce the development of a field-theoretic methodology which is able to predict on an equal footing electronic quasiparticles and phonons as well as their interaction. Such an approach has been implemented within the Quasiparticle Self-consistent GW (QSGW) formalism which describes well the electronic properties for a wide range of materials, including many where standard DFT fails. The reliability of a such field-theoretic methodology will be discussed with applications ranging from the renormalization of the optical gap of nonpolar semiconductors to the renormalization of the Fermi surface of correlated materials such as FeSe.