Mean-field approaches provide an understanding of ordered phases of matter. The excitations above such an ordered state can have nontrivial topological properties, like a finite Chern number and edge states. Furthermore, competing interactions in a quantum spin- and other strongly interacting systems can lead to entangled states that are beyond the reach of the traditional mean-field description — they may form different types of spin liquids with exotic excitations.

In this Ph.D. project, we will search for the ground states and excitations in spin liquids, non-conventional superconductors, interacting Rydberg atoms, artificial spin-ice, and other systems of current interest. This is primarily a theoretical study, requiring the application of analytical and numerical methods. At the same time, we will try to address questions relevant to experiments: for example, how can we excite non-abelian excitations? How do the excitations interact with light?