The functional renormalization group is a powerful method for studying correlated electron systems. It copes with competing interaction channels and hierarchies of energy scales over several orders of magnitude. The starting point for the application of the method is a functional flow equation for a generating functional, which allows to interpolate smoothly between the microscopic action and the full effective action of a model as a function of a flow parameter. In this talk, I will outline the derivation of flow equations for generating functionals and how to obtain flow equations for vertex functions. In order to make their solution numerically feasible, approximation schemes for the vertex are required, for which the so-called N-patch approximation and a channel-decomposition scheme are discussed as examples. Moreover, I will comment on conditions for the applicability of one-loop flows.

Max Planck Inst. for Solid State Research, Stuttgart, Germany