Computational Quantum Materials

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The so-called strong correlation problem has been the focus of intense research over the last decades. While it is often possible to describe a single quantum particle it is much more difficult to predict the behavior of several particles if these interact and have to correlate their behavior in particular if the interaction gives rise to frustration. Eventually, such correlation effects can dominate the physics and we talk about strongly correlated systems. A class of materials exists for which such correlation effects are crucial and leads to the presence of novel and exotic phases with surprising properties. Immediately, the following questions arise. What are these phases and how can we characterize their properties and understand the associated quantum phase transitions ? If excitations are created away from the ground-state what are these excitations and how can be described them and if a material is prepared in an excited state how will it reach equilibrium ? If we for a moment neglect interactions and instead consider the effect of disorder, which for many materials is inherently present or can easily be introduced, then one might expect glassy phases to appear and such phases have been shown to occur in a number of models. It is then natural to ask the very difficult question: What happens when both disorder and strong correlations are present ? How does a single impurity become entangled with the many-body state of the rest of the system and what new phases can appear ? In many cases the only way to answer all of these questions is through the use of state of the art computational method and this proposal aims to do that. The subtleness of these new phases and materials require new tools for describing and for studying them numerically. Fortunately, concepts from the field of quantum information and ideas from quantum optics have led to many exciting new developments in the field of condensed matter. Chief among these developments are new advanced numerical methods that allows us to characterize such new phases in quantum materials and detect the subtle quantum phase transitions that had previously gone un-noticed. The present proposal aims to use these new computational techniques for the study of quantum materials with the goal of answering the questions raised above. This will lead to key new insights of quantum materials and significantly advance our ability to perform advanced computational simulations.