Field-Driven Phenomena in 2-d and 3-d Kitaev Magnets

Kitaev's honeycomb model is an exactly solvable spin model that realises a quantum spin liquid ground state, with fractionalised excitations in the form of Majorana fermions and plaquette flux excitations. Recent studies have shown that applying an external magnetic field can give rise to a rich set of field-driven phenomena, including the appearance of a gapless U(1) spin liquid. However, the Kitaev model is not unique to the honeycomb lattice, the model can in fact be defined, and exactly solved, on a range of tri-coordinated lattices in two and three dimensions. This naturally provides an enormous playground within which to study field-driven phenomena in quantum spin liquids. We will discuss a number of examples and construct a generic phase diagram for the Kitaev model in the presence of a magnetic field.