Kugler, Fabian B.; Delft, Jan von
(2018):
Derivation of exact flow equations from the selfconsistent parquet relations.
In: New Journal of Physics, Vol. 20, 123029

Abstract
We exploit the parquet formalism to derive exact flow equations for the twoparticlereducible fourpoint vertices, the selfenergy, and typical response functions, circumventing the reliance on higherpoint vertices. This includes a concise, algebraic derivation of the multiloop flow equations, which have previously been obtained by diagrammatic considerations. Integrating the multiloop flow for a given input of the totally irreducible vertex is equivalent to solving the parquet equations with that input. Hence, one can tune systems from solvable limits to complicated situations by variation of oneparticle parameters, staying at the fully selfconsistent solution of the parquet equations throughout the flow. Furthermore, we use the resulting differential form of the SchwingerDyson equation for the selfenergy to demonstrate oneparticle conservation of the parquet approximation and to construct a conserving twoparticle vertex via functional differentiation of the parquet selfenergy. Our analysis gives a unified picture of the various manybody relations and exact renormalization group equations.