Emergent symmetries and phases in quantum 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 scenario to describe such systems is to consider the effect of an external control with a definite period in time that can act either locally or globally on the system of interest. However, apart from periodicity, such drives typically lack classical correlations or additional structure. In this work, we consider drives with intrinsic dynamics that undergo self-organization, leading to periodic steady states with emergent symmetries. To substantiate our results, we consider two examples of one-dimensional quantum spin chains coupled to a classical Kuramoto model. First, we investigate a Kuramoto model with all-to-all coupling driving a one-dimensional quantum Ising chain into a time-periodic steady state with an emergent translational symmetry. Next, we consider a Kuramoto model in a zigzag lattice driving an XX spin chain. The dynamics of traveling waves in the Kuramoto model trimerizes the lattice, effectively inducing topological behavior that can be exploited to perform topological pumping. Our results can be experimentally implemented in digital and analog near-term quantum devices.