Functional renormalization group for effective low-energy interactions

by Carsten Honerkamp, RWTH Aachen

Tuesday 8 May 2018, 16:00 → 17:00 Europe/Berlin

Room 222 (Jungiusstr. 9)

We first present recent results regarding the quantitative benchmarking of the functional renormalization group in the two-dimensional Hubbard model which indicate that the approach can become a quantitative method. Then we discuss the use of the constrained fRG (cfRG) in computing effective low-energy interactions in multiband systems, going beyond the well-known constrained random phase approximation (cRPA). We develop an efficient approximation for the electron-electron interaction in multi-orbital lattice systems. In this we describe the interaction as arising from the non-local and orbital-dependent coupling of particle-hole bilinears and particle-particle bilinears whose constituents reside in the same orbital. This allows us to employ a rather fine momentum discretization which e.g. gives insights on the non-local screening of spin and charge interactions. Using this formalism we compute the effective low-energy interactions in a three-band model where the two bands away from the Fermi levels are integrated out with cfRG. We show that the cfRG adds important features to the effective model that cannot be found using the cRPA.