The experimental and theoretical investigation of quantum spin systems has become one of the central disciplines of contemporary condensed matter physics. From an experimental
viewpoint, the field has been significantly fueled by the recent synthesis of novel strongly correlated materials with exotic magnetic or quantum paramagnetic ground states. From a
theoretical perspective, however, the numerical treatment of realistic models for quantum magnetism in two and three spatial dimensions still constitutes a serious challenge. This
particularly applies to frustrated systems, which complicate the employment of established methods. After a brief review of some basic concepts of quantum magnetism this talk gives an
introduction into the pseudofermion functional renormalization group (PFFRG) as a novel approach to determine large size ground state correlations of a wide class of spin
Hamiltonians. Using a diagrammatic pseudofermion representation for quantum spin models, the PFFRG performs systematic summations in all two-particle fermionic interaction channels,
capturing the correct balance between classical magnetic ordering and quantum fluctuations. Numerical results for various frustrated spin models on different lattices are presented and
benchmarked against other methods if available. Furthermore, recent applications to novel magnetic materials in the context of the search for quantum spin liquids are discussed.