Project leader: Alessandro Toschi
Funding institution: 
Austrian Science Fund
Project number: I610-N16
Project duration: October 2011 - September 2016
QCM - Quantum criticality in strongly correlated magnets
One of the most fascinating physical phenomena is quantum criticality and the connected non-Fermi-liquid behavior, a topic at the forefront of condensed matter physics. Experimentally, quantum criticality is often realized in materials where electrons are strongly correlated. Despite some progress brought about, e.g., through perturbation theory, the concept of local quantum criticality and extended dynamical mean field theory (eDMFT), our understanding and theoretical modeling of this fundamental phenomenon is still unsatisfactory.
Recently, the applicants developed a complementary extension of dynamical mean-field theory based on Feynman diagrams and coined dynamical vertex approximation (DΓA). In contrast to eDMFT which accounts for local correlations induced by non-local interactions, DΓA describes non-local correlations originating from a local interaction. We hold that these non-local correlations are of essential importance at a quantum critical point which is typically connected with the onset of long-range magnetic ordering. As a consequence, long-range correlations are unavoidable at a magnetic quantum critical point. Hence, a combination of long-range spatial fluctuations and longtime quantum fluctuations will ultimately determine the critical behavior and the critical exponents at a quantum critical point. These effects are included in DΓA on an equal footing, which, at the same time, also describes correlation induced renormalization effects and transitions such as the Fermi surface collapse observed in experiment and in the scenario of local quantum criticality. This collapse is connected with the formation of local magnetic moments, which we also plan to study in the framework of the proposed project.
Owing to these circumstances, we feel the application of a new method, DΓA, offers a unique opportunity to most substantially improve our understanding of quantum criticality and to realistically model relevant materials. As the project strikes a new route to describe quantum criticality by employing a new method, DΓA, it bears the potential for a truly high-impact.