We study periodically driven closed quantum systems where two parameters of the system Hamiltonian are varied periodically in time with frequencies ${\omega }_1$ and ${\omega }_2=r{\omega }_1$. We show that such drives may be used to tune towards dynamics-induced freezing where the wave function of the state of the system after a drive cycle at time $T=2\pi /{\omega }_1$ has almost perfect overlap with the initial state. We locate regions in the $({\omega }_1,r)$ plane where the freezing is near exact for a class of integrable models and a specific nonintegrable model. The integrable models that we study encompass Ising and $\mathit{XY}$ models in $d=1$, Kitaev model in $d=2$, and Dirac fermions in graphene and atop a topological insulator surface, whereas the nonintegrable model studied involves the experimentally realized one-dimensional tilted Bose-Hubbard model in an optical lattice. In addition, we compute the relevant correlation functions of such driven systems and describe their characteristics in the region of the $({\omega }_1,r)$ plane where the freezing is near exact. We supplement our numerical analysis with semianalytic results for integrable driven systems within adiabatic-impulse approximation and discuss experiments which may test our theory.

• Received 14 May 2016

DOI:https://doi.org/10.1103/PhysRevB.94.075130