Functional renormalization group approach to low-energy effective interactions in multi-band many-fermion systems

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We propose to extend and apply a recently developed functional renormalization group (fRG) scheme to compute low-energy effective interactions in multiband many-fermion systems, where the effects of higher-energy bands are absorbed into the effective interactions in one or few low-energy band. This fRG scheme includes and extends the constrained-RPA (cRPA) approach that has been used fruitfully in many different material systems as a tool to compute the interaction parameters of extended Hubbard models for the description of the bands near the Fermi level. We argue that with the new fRG scheme, we can assess the validity of the cRPA by summing more than just a particular class of diagrams. A first application in a toy model (published in Phys. Rev. B) revealed that there are indeed parameter regimes where cRPA and the less ad-hoc fRG approach give different results, both with respect to the frequency structure of the effective interaction as well as regarding the average suppression of the bare repulsion. The current project now aims atimproving the implementation of the fRG scheme such that more realistic models can be tackled and that a more detailed picture of the effective interactions beyond cRPA can be obtained. The key ansatz that should allow us to treat realistic models is a suitable decomposition of the wavevector- and frequency dependence of the interactions that has previously been used for the study of one-band Hubbard and impurity models. We give feasibility arguments that the numerical effort is tractable using this decomposition. First applications will address models for graphene, for which we argue that a more refined determination of effective interaction parameters may be important for a correct and satisfactory description of correlation effects. For this project at the interface between methodical development in many-particle physics and key materials in current solid physics we request the funding of one Ph.D. positions for 36 months.