Dynamical vertex functions of many-electron systems

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Wider research context - Our project aims at a substantial advancement in the quantum field theory description of the many-electron problem. We focus on one of the most challenging theoretical aspects: the physics of two-particle scattering processes in correlated quantum materials. In the realm of the Feynman diagrammatic these processes are described by the vertex-functions, i.e. the analog of the self-energy on the two-particle level.Level of originality/innovation - Mastering the vertex functions, similarly as it is presently possible for the self- energy, represents a pivotal step for the many-body theory of interacting fermions and for a complete understanding of the underlying physics. Further, it will significantly raise the predictive power of realistic calculations of spectroscopic and transport properties of quantum materials.Research questions/objectives - The first objective of our program is the investigation of the physical and algorithmic impact of the divergences of the irreducible vertex functions, recently discovered to occur in basic models of correlated electrons. These anomalies, associated to an underlying multivaluedness of the Luttinger-Ward functionals, challenge the current theoretical understanding in several fundamental aspects. We plan thorough studies of increasing physical complexity, designed to unveil the true role played by these divergences, hitherto understood only at a mere formal level.Our second goal deals with the effects of two-particle correlations in physical response functions: the vertex corrections. Due to their numerical complexity, these are often neglected or severely approximated. We will fill a relevant gap of the current literature, by working out the general conditions under which vertex corrections are no longer symmetry-forbidden and have to be taken into account in model and material calculations. Then, we will analyze the largely unexplored phenomenology induced by vertex corrections to dynamical susceptibilities and conductivities, calculating them within state-of-the-art many-body methods for cases of special physical interest.In the final stage of the project, we will extend the vertex formalism to systems with reduced symmetry, including also spin-orbit coupling effects and long-range ordered phases. This will allow for a full “theoretical spectroscopy” of magnetic as well as topological materials, investigated so far within weak-coupling approximations only.Methods - Our planned research will rely on advanced many-body approaches such as multi-orbital dynamical mean-field theory and its extensions and, where needed, on semi-analytic or diagrammatic calculations.Primary researcher involved - The ambitious scientific agenda of this project will be made possible by the joint expertise of the two PIs involved (Alessandro Toschi and Giorgio Sangiovanni), greatly profiting from the long-standing cooperation between their groups.