Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids

Abstract: We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian topological spin liquids. 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 engineer 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. Our findings shed light on the nonequilibrium physics of driven topologically ordered quantum matter and may facilitate the observation of non-Abelian behaviour in engineered quantum systems.