Quantum fingerprints of self-organization in spin chains coupled to a Kuramoto model

Floquet theory is a widely used framework to describe the dynamics of periodically-driven quantum systems. The usual set up to describe such kind of systems is to consider the effect of an external control with a definite period in time that can act either globally or locally on the system of interest. However, besides the periodicity, there is no classical correlation or other well defined structures in the drive. In this work, we consider drives that exhibit self-organization phenomena reaching periodic steady states with emergent symmetries. To substantiate our results, we consider two examples of a one-dimensional quantum spin chains in a transverse field coupled to a classical Kuramoto model. In the case of all-to-tall coupling, the Kuramoto model drives the Ising chain into a time-periodic steady state with an emergent translational symmetry. For a Kuramoto model in a Zig-zag lattice, the XX spin chain is trimerized and the dynamics exhibit topological behavior that can be exploited to perform topological pumping. Our results can be experimentally implemented in near-term quantum devices in digital and analog platforms.