  Driving a quantum system periodically in time can profoundly alter its
long-time correlations and give rise to exotic quantum states of matter. The
complexity of the combination of many-body correlations and dynamic
manipulations has the potential to uncover a whole field of new phenomena, but
the theoretical and numerical understanding becomes extremely difficult. We now
propose a promising numerical method by generalizing the density matrix
renormalization group to a superposition of Fourier components of periodically
driven many-body systems using Floquet theory. With this method we can study
the full time-dependent quantum solution in a large parameter range for all
evolution times, beyond the commonly used high-frequency approximations.
Numerical results are presented for the isotropic Heisenberg antiferromagnetic
spin-1/2 chain under both local(edge) and global driving for spin-spin
correlations and temporal fluctuations. As the frequency is lowered, we
demonstrate that more and more Fourier components become relevant and determine
strong length- and frequency-dependent changes of the quantum correlations that
cannot be described by effective static models.
