Energies and spectra of solids from the algorithmic inversion of localized \(GW\)

Energy functionals of the Green's function can provide simultaneously spectral and thermodynamic properties of interacting electrons' systems. Exploiting a localized-GW approach, we introduce an approximation to the exchange-correlation part of the Klein functional that generalizes the energy functional of DFT+U to host a dynamical screened potential \(U(\omega)\). Furthermore, we solve exactly the resulting Dyson equation extending to crystals the algorithmic-inversion method. We then compute the spectral, thermodynamic, and vibrational properties of SrVO\(_3\), finding results in close agreement with experiments and state-of-the-art computational methods, at very reduced computational costs.