A Functional Renormalization Scheme for the Many-electron Problem

We re-structure the perturbative renormalization scheme, which has been widely used in particle physics to solve local quantum field theories, in the context of the many-electron problem. This new functional renormalization scheme provides a systematic framework to study the emergent properties driven by non local quasiparticle interactions. This type of problem has been notoriously difficult to solve with many existing numerical techniques (e.g., functional renormalization group, and diagrammatic Monte Carlo, diagrammatic extensions of dynamical mean-field theory). We use this scheme to determine the momentum-resolved charge and spin response functions of the uniform electron gas. The high accuracy of our calculation uncovers several fine structures in these response functions for the first time.