Controlling the dynamics of quantum many-body systems is crucial for developing quantum technologies. This work demonstrates that counterdiabatic (CD) driving provides a powerful tool for steering collective spin systems along entangled trajectories for a long time. In particular, CD driving leads to approximate stroboscopic freezing and eternal entanglement oscillations for a large class of initial states in the periodically driven Lipkin-Meshkov-Glick model. Intriguingly, CD driving generates spin squeezing and its associated metrologically useful multipartite entanglement at the mid-point of every drive cycle, when the system is initially prepared in a fully $x$-polarized state. The CD driving induced nonergodic dynamics is accompanied by a decrease in the average eigenstate entanglement and inverse participation ratio, thereby signaling greater eigenstate localization. Our work opens a new route to evade Floquet heating and control entanglement generation in collective spin systems.

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• Quantum control
• Quantum protocols
• Floquet systems