Fig. 3: Dynamics of a single spin inhomogeneity in the localized, ergodic, swappy, and near-SWAP regimes of the model.

Results of numerical propagation of the initial spin inhomogeneity in the M = 0 sector under U(1)-symmetric Floquet dynamics at N = 20. a–d show typical results for single realizations of the initial state and Floquet unitary within the localized regime, ergodic regime, and two points in the swappy regime, respectively. e–h show results in the respective regimes after averaging over 100 realizations. Horizontal lines indicate the time taken to complete a single Floquet cycle (solid), N/2 (dashed), and the time after which we calculate results stroboscopically (dotted). Although the light cones in (b, f) visually show the excitation spreading and an apparent equilibration for t between \({\mathcal{O}}(N)\) and \({\mathcal{O}}({N}^{2})\), we confirm diffusive transport quantitatively in the following sections. An analysis of what happens exactly on the light-cone is offered in Sec. S3 of the SM.