Floquet time spirals and stable discrete-time quasicrystals in quasiperiodically driven quantum many-body systems

We analyze quasiperiodically driven quantum systems that can be mapped exactly to periodically driven ones and find Floquet time spirals in analogy with spatially incommensurate spiral magnetic states. Generalizing the mechanism to many-body systems, we discover that a form of discrete-time translation symmetry breaking can also occur in quasiperiodically driven systems. We construct a discrete-time quasicrystal stabilized by many-body localization. Crucially, it persists also under perturbations that break the equivalence with periodic systems. As such, it provides evidence of a stable quasiperiodically driven many-body quantum system which does not heat up to the featureless infinite-temperature state.