One of the central tasks in condensed matter physics is to identify different possible states of matter. In addition to the everyday categories of solid, liquid and gas, many additional states arise when we consider degrees of freedom other than the positions of atoms. In magnetic materials the relevant degrees of freedom are atomic magnetic moments, and magnetic states of matter are distinguished by the behaviour of these moments. Many magnetic materials have low-temperature states in which the atomic magnetic moments are ordered, like atoms in a crystal. Geometrical frustration is interesting as a way of making something different happen. Frustrated magnets have interactions that compete with each other, and fluctuate between many different states even at low temperature. In this sense they provide an analogue for magnetic systems of the liquid phase of ordinary matter. Spin liquids, however, turn out to be much more interesting in important ways than ordinary liquids: in their low-energy states the microscopic magnetic moments are dissolved by fluctuations and re-form as new degrees of freedom, often involving emergent gauge fields and fractionalised quasiparticles. I aim to present a simple overview of ideas in this field and to summarise some recent work on the dynamics of a remarkably simple, exactly solvable model -- the Kitaev honeycomb model -- that has a spin liquid ground state.
John Chalker was awarded a BA in Theoretical Physics from the University of Cambridge and a DPhil from the University of Oxford, where his advisor was Gillian Gehring. He worked as a Research Fellow in Franz Wegners group at Heidelberg University before becoming a faculty member at Southampton University. He joined the condensed matter theory group at Oxford in 1991, where he is now Professor of Physics. His research has covered many aspects of the quantum and statistical physics of condensed matter, including particularly quantum Hall systems, disordered conductors, and the statics and dynamics of frustrated magnets.