Chiral Parafermions in Floquet ℤN 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 ℤN 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 ℤN 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 ℤN Kitaev models as a setting for exploring intrinsically non-equilibrium topological phenomena on qudit-based quantum processors.
Related
- Probing chiral topological order of the Kitaev honeycomb on a trapped ion processor
- Collinear altermagnetism for 3D chiral higher-order topological insulators
- Invertible subalgebras for chiral semion topological order
- Detuning the Floquet anomalous chiral spin liquid
- From Approximate Floquet Engineering to Full Floquet Theory: Coherent Control of Chiral Spin Systems in Spintronics
BibTeX
@misc{will2026chiral,
title = {{Chiral Parafermions in Floquet $\mathbbZ_N$ Topological Order}},
author = {Melissa Will and Harald Schmid and Jan Egger and Adam Gammon-Smith and Michael Knap and Frank Pollmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07156},
eprint = {2610.07156},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07156},
}
RIS
TY - UNPB
TI - Chiral Parafermions in Floquet ℤ_N Topological Order
AU - Melissa Will
AU - Harald Schmid
AU - Jan Egger
AU - Adam Gammon-Smith
AU - Michael Knap
AU - Frank Pollmann
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07156
UR - https://arxiv.org/abs/2610.07156
AB - Floquet topological order (FTO) extends topology beyond equilibrium, giving rise to phenomena, such as the dynamical transmutation of anyons. Here, we realize 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 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 ℤ_N Kitaev models as a setting for exploring intrinsically non-equilibrium topological phenomena on qudit-based quantum processors.
ER -