The ordered phases of magnetic materials are usually well understood within the framework of the mean-field approaches. However, competing interactions in quantum spin system can lead to entangled states which are beyond the traditional mean-field description. In such systems the order is often lost — they form the wide class of spin liquids. In other cases, the excitations above a trivial state have nontrivial topological properties, like a finite Chern number and edge states.
Good knowledge of mathematical methods like group theory and linear algebra, of quantum mechanics and most importantly, enthusiasm and interest in pursuing a difficult, but rewarding problem.