Chiral Parafermions in Floquet ${\mathbb{Z}}_N$ Topological Order

Abstract

Floquet topological order (FTO) extends topology beyond equilibrium, giving rise to phenomena, such as the dynamical transmutation of anyons. Here, we realize ${\mathbb{Z}}_N$ FTO in a generalized Kitaev honeycomb model with clock degrees of freedom using a three-step periodic drive. The driven system admits an emergent description in terms of constrained parafermions coupled to conserved ${\mathbb{Z}}_N$ gauge fields. At the boundary, the drive generates chiral parafermionic Floquet edge modes. We resolve their propagation through correlation functions, characterize their fractional quantum-information transport through the radical chiral unitary index, and use their dynamics to probe exchange statistics. In the bulk, we explore the dynamical anyon transmutation with a non-equilibrium loop order parameter. At a Floquet sweet spot, where the drive becomes Clifford, these phenomena can be accessed using stabilizer simulations. Short-time matrix-product-state simulations away from this point show that the chiral edge response persists at accessible times. Our results establish ${\mathbb{Z}}_N$ Kitaev models as a setting for exploring intrinsically non-equilibrium topological phenomena on qudit-based quantum processors.

7+7 pages, 5+3 figures