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.
Johannes Reuther did his undergraduate studies at the KIT, Germany where he received his masters degree in 2007. He continued doing a PhD at KIT in theoretical condensed matter physics under the supervision of Prof. Peter Woelfle. During his time as a PhD student he started developing functional renormalization group methods for quantum spin systems. After receiving his PhD in 2011, he was awarded a Leopoldina Postdoc fellowship that enabled him to do postdoctoral research first at the UC Irvine (2012) and later at the Caltech (2012-2014). At both places, he worked on topological quantum systems and Majorana fermions, supervised by Prof. Jason Alicea. Since 2014 he holds an assistant professor position at Free University Berlin/Germany. He also is the head of the Berlin Joint Lab: Quantum Magnetism, a collaboration between Free University Berlin and Helmholtz Center Berlin for Materials and Energy (HZB) which bridges between theoretical and experimental research in the field of quantum magnetism.