Non-Abelian anyons in periodically-driven Abelian spin liquids

We present theoretical results about the emergence of non-Abelian anyons in an Abelian topologically-ordered system subject to local time-periodic driving. This effect is illustrated with a driven toric-code model. The Abelian anyons in the toric code include fermionic and bosonic quasiparticle excitations which see each other as $\pi$ fluxes, namely they result in the accumulation of a $\pi$ phase if wound around each other. Non-Abelian behaviour emerges because the Floquet modulation can induce a non-trivial band topology for the fermions, inducing their fractionalization into Floquet-Majorana modes bound to the bosons. The latter then develop non-Abelian character akin to vortices in topological superconductors, realizing Ising topological order. This effect is explained through high-frequency expansions in a quasiparticle picture and verified through explicit computation of the vortex exchange phases.