Strongly correlated systems
The interplay of strong inter-particle interactions, quantum fluctuations, and low temperature can lead to many interesting phenomena in condensed matter systems. Many of these are now well-understood in terms of standard theoretical paradigms such as Landau's Fermi Liquid Theory, the Bogoliubov description of superfluids, the BCS theory of superconductivity, spin-wave theory for magnetically ordered systems, and the scaling theory of localization in disordered electronic systems. However, there are many examples that do not fall into any of these known paradigms, and are therefore very poorly understood - examples include the unusual normal state of high-Tc superconductors, heavy fermion materials on the verge of a transition to a spin-density wave state and frustrated magnets with unusual spin-liquid ground states. Over the last few years, our work has focused on computational and analytical studies of the properties of frustrated magnets in which competing interactions lead to unusual `spin-liquid' ground states which can exhibit exotic properties, such as excitations with fractional quantum numbers.