We present a multiloop implementation of the functional renormalization group (fRG) based on the single boson exchange (SBE) decomposition applied to the two dimensional Hubbard model.
In the SBE diagrams of the two particle vertex are classified accoring to their reducibility in the bare interaction compared to the two-particle reducibility of the widely-used parquet decomposition. This allows for a substantial reduction of numerical effort by isolating divergences in the screened interactions and reducing the importance of the most cost intensive element, the rest function, to such a degree that it may be neglected in many cases.
In the multiloop fRG the Parquet approximation is recovered through an iterative procedure. We analyze the Yukawa couplings and screened interactions and rest functions with increasing loop order and the influence the rest function has on observables such as the self energy and susceptibilities.