  We investigate the spectral properties and dynamical features of a
time-periodic PT-symmetric Hamiltonian on a one-dimensional tight-binding
lattice. It is shown that a high-frequency modulation can drive the system
under a transition between the broken-PT and the unbroken-PT phases. The
time-periodic modulation in the unbroken-PT regime results in a significant
broadening of the quasi-energy spectrum, leading to a hyper-ballistic transport
regime. Also, near the PT-symmetry breaking the dispersion curve of the lattice
band becomes linear, with a strong reduction of quantum wave packet spreading.
