In a class of periodically driven systems, multifractal states in nonequilibrium conditions and robustness of dynamical localization when the driving is made aperiodic have received considerable attention. In this paper, we explore a family of one-dimensional Aubry-André-Harper models that are quasiperiodically kicked with protocols following different binary quasiperiodic sequences, which can be realized in ultracold atom systems. The relationship between the systems' localization properties and the sequences' mathematical features is established utilizing the Floquet theorem and the Baker-Campbell-Hausdorff formula. We investigate the multifractality and prethermalization of the eigenstates of the unitary evolution operator combined with an analysis of the transport properties of initially localized wave packets. We further contend that the quasiperiodically kicked Aubry-André-Harper model provides a rich phase diagram as the periodic case but also brings the range of parameters to observe multifractal states and prethermalization to a regime more amenable to experiments.

• Received 9 November 2023
• Accepted 17 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.054202