Quantum criticality in strongly correlated magnets (QCM)

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 (DGA). In contrast to eDMFT which accounts for local correlations induced by non-local interactions, DGA 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 on an equal footing in DGA, 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, DGA, 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, DGA, it bears the potential for a truly high-impact.

The project goal was to study the physics of quantum critical magnetic transitions in strongly correlated systems. This subject is of high relevance for the cutting-edge research in condensed matter physics because, in contrast to the classical (finite-temperature) phase transitions, some of which encountered in the all-day life, the phenomenology of transitions occurring at zero temperature is dominated by quantum effects. This challenges our theoretical understanding, making hard to formulate reliable predictions, for exploiting, e.g., the physical properties of such transitions in future material design. Further, several among the most interesting quantum phase transitions occur in physical systems, where the electronic interaction is too weakly screened to be neglected, rendering the conventional band-theory not applicable even at finite-temperature. In the course of the project, significant progress has been achieved in this direction: Through the application, and the further development, of cutting-edge algorithms to treat systems of strongly interacting electrons, it was possible to investigate the physics of their phase transitions both at finite and at zero temperature. In particular, as for the latter ones, the numerical calculations performed at the TU Vienna, supported by a parallel analytical studies made in Yekaterinburg (Russia), have demonstrated the emergence of unexpected microscopic mechanisms: The physical behavior at the quantum phase transitions of strongly correlated electrons in three dimensions is controlled by the geometrical properties of the underlying Fermi surface, due to the disappearance of the corresponding thermal fluctuations. The generic nature of this result goes well beyond the calculations performed in our project, introducing a new essential ingredient for the future analysis of experiments in quantum critical systems. At the same time, the algorithmic advances obtained during the project, are made available to the scientific communities working on strongly correlated systems through the presentation in review works and planned publication of the corresponding source codes. In particular, the community will benefit from the explicit discussion some of unexpected algorithmic and conceptual difficulties encountered in the course of the project and the presentation of the corresponding solution-paths. This will help to improve the predictivity of forefront computational material calculations in presence of strongly coupled electrons, also beyond the quantum critical regime, a crucial prerequisite for a future large-scale industrial usage of correlated electronic compounds.