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.
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Publication details
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Cite this article
APA 7
Will, M., Schmid, H., Egger, J., Gammon-Smith, A., Knap, M., & Pollmann, F. (2026). Chiral Parafermions in Floquet $\mathbb{Z}_N$ Topological Order. https://omanscience.com/en/articles/chiral-parafermions-in-floquet-mathbb-z-n-topological-order
MLA 9
Will, Melissa, et al. "Chiral Parafermions in Floquet $\mathbb{Z}_N$ Topological Order." https://omanscience.com/en/articles/chiral-parafermions-in-floquet-mathbb-z-n-topological-order.
Chicago (author–date)
Will, Melissa, Harald Schmid, Jan Egger, Adam Gammon-Smith, Michael Knap, and Frank Pollmann. 2026. "Chiral Parafermions in Floquet $\mathbb{Z}_N$ Topological Order." https://omanscience.com/en/articles/chiral-parafermions-in-floquet-mathbb-z-n-topological-order.
Harvard
Will, M., Schmid, H., Egger, J., Gammon-Smith, A., Knap, M. and Pollmann, F. (2026) 'Chiral Parafermions in Floquet $\mathbb{Z}_N$ Topological Order', Available at: https://omanscience.com/en/articles/chiral-parafermions-in-floquet-mathbb-z-n-topological-order.
Vancouver
Will M, Schmid H, Egger J, Gammon-Smith A, Knap M, Pollmann F. Chiral Parafermions in Floquet $\mathbb{Z}_N$ Topological Order. https://omanscience.com/en/articles/chiral-parafermions-in-floquet-mathbb-z-n-topological-order
IEEE
M. Will, H. Schmid, J. Egger, A. Gammon-Smith, M. Knap, and F. Pollmann, "Chiral Parafermions in Floquet $\mathbb{Z}_N$ Topological Order," https://omanscience.com/en/articles/chiral-parafermions-in-floquet-mathbb-z-n-topological-order.