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Driving a quantum system periodically in time can profoundly alter itslong-time correlations and give rise to exotic quantum states of matter. Thecomplexity of the combination of many-body correlations and dynamicmanipulations has the potential to uncover a whole field of new phenomena, butthe theoretical and numerical understanding becomes extremely difficult. We nowpropose a promising numerical method by generalizing the density matrixrenormalization group to a superposition of Fourier components of periodicallydriven many-body systems using Floquet theory. With this method we can studythe full time-dependent quantum solution in a large parameter range for allevolution times, beyond the commonly used high-frequency approximations.Numerical results are presented for the isotropic Heisenberg antiferromagneticspin-1/2 chain under both local(edge) and global driving for spin-spincorrelations and temporal fluctuations. As the frequency is lowered, wedemonstrate that more and more Fourier components become relevant and determinestrong length- and frequency-dependent changes of the quantum correlations thatcannot be described by effective static models.

Periodically Driven Many-Body Systems: A Floquet Density Matrix Renormalization Group Study