Title: Integrable Floquet dynamics,
Abstract: We discuss several classes of integrable Floquet systems, i.e. systems which
do not exhibit chaotic behavior even under a time dependent perturbation. The
first class is associated with finite-dimensional Lie groups and
infinite-dimensional generalization thereof. The second class is related to the
row transfer matrices of the 2D statistical mechanics models. The third class
of models, called here "boost models", is constructed as a periodic interchange
of two Hamiltonians - one is the integrable lattice model Hamiltonian, while
the second is the boost operator. The latter for known cases coincides with the
entanglement Hamiltonian and is closely related to the corner transfer matrix
of the corresponding 2D statistical models. We present several explicit
examples. As an interesting application of the boost models we discuss a
possibility of generating periodically oscillating states with the period
different from that of the driving field. In particular, one can realize an
oscillating state by performing a static quench to a boost operator. We term
this state a "Quantum Boost Clock". All analyzed setups can be readily realized
experimentally, for example in cod atoms.