Micromotion in Floquet Prethermalization via dynamical space-time symmetries

We present a systematic framework for Floquet prethermalization under strong resonant driving, emphasizing the pivotal role of dynamical space-time symmetries and building upon previous work [1] that revealed novel quasi-energy gap-dependent classifications arising from these symmetries. Our approach demonstrates how these dynamical space-time symmetries map onto the projective static symmetry group of the prethermal Hamiltonian governing the prethermal regime. Techniques for detecting dynamical symmetries through the time evolution of local observables facilitate a detailed analysis of micromotion within each period, surpassing the limitations of conventional stroboscopic Floquet prethermal dynamics. To implement this framework, we designed a prethermal protocol that preserves order-two dynamical symmetry in a spin-ladder model, confirming the predicted relationships between the expectation values of local observables at distinct temporal points in the Floquet cycle, which are linked by this symmetry. Notably, this detection protocol imposes no constraints on the initial state, significantly enhancing its experimental feasibility.