Multi-loop contributions in the pseudo-fermion functional renormalization group for quantum spin systems: implementation and consequences*

We extend the pseudo-fermion functional renormalization group (PFFRG) treatment of quantum spin systems by including diagrammatic higher loop contributions into the renormalization group flow. This allows us to consistently account for all contributions of parquet-type diagrams in the two-particle vertex and self-energy derivatives within the two-particle truncated PFFRG flow. We will discuss the impact of these corrections in different quantum spin models within PFFRG, especially in the light of the Mermin-Wagner theorem.