Addressing quantum embedding via the algorithmic inversion of dynamical potentials

Quantum embedding formulations are used to describe physical systems immersed in a bath. Frequency-dependent potentials are needed to couple the two systems and appear in embedding formalisms such as many-body perturbation theory, dynamical mean-field theory, electron-boson coupling, or spectral potentials. Once formulated (e.g., via. many-body perturbation theory), the solution at all frequencies of non-linear-Dyson-like equations is needed to retrieve spectral and thermodynamic quantities for the system studied. Here we apply the algorithmic inversion method to solve exactly and at all frequencies Dyson-like equations for homogeneous systems, with application to the homogeneous electron gas, and discuss the extension to non-homogeneous systems.