  Topological states of matter present a wide variety of striking new
phenomena. Prominent among these is the fractionalisation of electrons into
unusual particles: Majorana fermions [1], Laughlin quasiparticles [2] or
magnetic monopoles [3]. Their detection, however, is fundamentally complicated
by the lack of any local order, such as, for example, the magnetisation in a
ferromagnet. While there are now several instances of candidate topological
spin liquids [4], their identification remains challenging [5]. Here, we
provide a complete and exact theoretical study of the dynamical structure
factor of a two-dimensional quantum spin liquid in gapless and gapped phases.
We show that there are direct signatures - qualitative and quantitative - of
the Majorana fermions and gauge fluxes emerging in Kitaev's honeycomb model.
These include counterintuitive manifestations of quantum number
fractionalisation, such as a neutron scattering response with a gap even in the
presence of gapless excitations, and a sharp component despite the
fractionalisation of electron spin. Our analysis identifies new varieties of
the venerable X-ray edge problem and explores connections to the physics of
quantum quenches.
