Dynamical Generation of Interactions and Floquet Skyrmions in Periodically Driven Spin Systems

Motivated by applications in synthetic quantum simulators, we study many-body Floquet spin systems with periodically driven two-body interactions and external fields in the high-frequency limit. We show that a hierarchy of multi-spin interactions can be generated in powers of inverse-frequency, such as Dzyaloshinskii–Moriya interaction (DMI), three- and four-spin interactions, and additional Zeeman terms. We consider different types of drives and lattice geometries in one and two dimensions to explore possible types of dynamically generated interactions. In particular, we focus on the DMI term in two-dimensional square and triangular lattices to study the dynamical generation of quantum skyrmions, controlled by drive parameters. Using exact diagonalization and hierarchical mean-field theory calculations, we characterize the energetic and topological signatures of possible skyrmion phases. This study is relevant to the experimental realization of Floquet skyrmion, for example, in recently demonstrated two-dimensional lattices of trapped ions.