Exact renormalization group and Phi-derivable approximations

Abstract

We show that the so-called Phi-derivable approximations can be combined with the exact renormalization group to provide efficient non-perturbative approximation schemes. On the one hand, the Phi-derivable approximations allow for a simple truncation of the infinite hierarchy of the renormalization group flow equations. On the other hand, the flow equations turn the non linear equations that derive from the Phi-derivable approximations into an initial value problem, offering new practical ways to solve these equations.

15 pages, 2 figures

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• Results from the 4PI Effective Action in 2- and 3-dimensions
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• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems