Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes

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, Laughlin quasiparticles or
magnetic monopoles. 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, their identification remains
challenging. 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.