Electronic correlations on the three-particle level

With Sheldon Cooper from Big Bang theory at the latest, the scribblings of theoretical physicists known as Feynman diagrams arrived in mainstream society. We can reduce the number of diagrams by introducing the concept of an irreducible vertex. The one-particle irreducible vertex, better known as self energy, describes life-time effects and renormalizations of the (quasi)particle mass. For two-particles, we understand through ladder diagrams, among others, magnons (the elementary excitations of a ferromagnetic) and the binding of a particle-hole pair to an exciton in a semiconductor. Three particle vertices and Feynman diagrammatics remain, so-far, a blank spot in the theory of strongly correlated electron systems. The aim of the present project is to explore this unknown, to develop the appropriate equations for three-particle vertex ladder and parquet diagrams, and to explore the associated three-particle physics. Physics that we cannot even imagine today. This endeavor further allows us to push the dynamical vertex approximation and the dual fermion approach, which assumes the locality of a n-particle vertex, to the next n=3 particle rung of the ladder.

Latest with Sheldon Cooper from Big Bang theory, the scribblings of theoretical physicists known as Feynman diagrams arrived in mainstream society. We can reduce the number of diagrams by introducing the concept of an irreducible vertex. The one-particle irreducible vertex, better known as self-energy, describes life-time effects and renormalizations of the (quasi)particle mass. For two particles, we understand through ladder diagrams, among others, magnons (the elementary excitations of a ferromagnet) and the binding of a particle-hole pair to an exciton in a semiconductor. Three-particle vertices and Feynman diagrammatics were hitherto a blank spot in the theory of strongly correlated electron systems. In the project Eco3P we developed the formalism of such three-particle vertex diagrammatics. We showed that genuine three-particle vertices are important, unexpectedly in particular for a chiral spin susceptibility. We further developed methods to calculate the local three-particle vertex exactly and approximately in a ladder approximation. The connection of the three-particle vertex and derived susceptibilities to experiments measuring non-linear, Raman and Hall response has been highlighted.