Transport through Periodically Driven Correlated Quantum Wires

We study correlated quantum wires subject to harmonic modulation of the onsite-potential concentrating on the limit of large times, where the response of the system has synchronized with the drive. We identify the ratio $\Delta\epsilon/\Omega$ of the driving amplitude $\Delta\epsilon$ and the frequency of driving $\Omega$ as the scale determining the crossover from a modified Luttinger liquid picture to a system that behaves effectively like a higher dimensional one. We exemplify this crossover by studying the frequency dependency of the boundary density of state $\rho_{\rm B}(\omega)$ as well as the temperature dependency of the linear conductance $G(T)$ through the wire, if the latter is contacted to leads. Both observables are known to exhibit Luttinger liquid physics without driving given by characteristic power-law suppression as $\omega\to\epsilon_{\rm F}$ (with $\epsilon_{\rm F}$ the Fermi energy) or $T\to 0$, respectively. With driving we find that this suppression is modified from a single power-law to a superposition of an infinite number of power laws. At small $\Delta\epsilon/\Omega\ll 1$ only a few terms of this infinite sum are relevant as the prefactors of higher terms are suppressed exponentially. Thus a picture similar to the equilibrium Luttinger liquid one emerges. Increasing $\Delta\epsilon/\Omega$ an increasing number of power laws contribute to the sum and approaching $\Delta\epsilon/\Omega\gg 1$ the system behaves effectively two dimensional, for which the suppression is wiped out completely.