Abstract

Periodic driving provides a powerful tool for the coherent control of quantum matter. In this talk, I will discuss two routes to realize dynamical many-body freezing in periodically driven quantum systems. In the first half of the talk, I will present a two-rate drive protocol that can be used to engineer exact Floquet flat bands in a large class of closed quantum many-body systems. This leads to perfect many-body freezing and implies a strong violation of the eigenstate thermalization hypothesis. In the second half of the talk, I will discuss a counter-diabatic (CD) driving protocol to realize dynamical many-body freezing and eternal entanglement oscillations in the periodically driven Lipkin-Meshkov-Glick model. More generally, CD driving leads to Floquet eigenstates with anomalously low entanglement and consequently a lowering of the average eigenstate entanglement. These results suggest that CD driving protocols can provide a powerful route to realize long-lived Floquet phases of matter.