Energies and spectra of correlated metals via the algorithmic inversion of dynamical potentials

Dynamical (frequency-dependent) potentials are needed to predict accurate spectral properties, and arise in embedding theories. The frequency dependence transforms the problem from the diagonalization of an operator (e.g., the Kohn-Sham Hamiltonian of density-functional theory) to the Dyson inversion of a self-energy. Here, we propose a novel treatment of dynamical potentials able to solve Dyson-like equations via an exact mapping to an effective non-interacting problem. The sum-over-poles representation of the self-energy, together with the static contribution to the Hamiltonian, are used to build a (larger) effective Hamiltonian that has the excitation energies of the system as eigenvalues and the Dyson orbitals as a projection of the eigenvectors. The Green's function of the system is also obtained as a sum over poles, and allows for the computation of both spectral and thermodynamic properties. To explore applications on real materials, we introduce a localized-GW Klein functional exploiting the frequency-resolved screened-potential U(ω), and we apply it to calculate the spectral and mechanical properties of SrVO₃.