Local-to-Global Entanglement Dynamics by Periodically Driving Impurities

We study the entanglement dynamics of a one-dimensional spin chain subject to a local Floquet drive of a two-site impurity. We uncover a sharp transition in the entanglement dynamics as a function of the driving frequency. For large drive periods T, we observe a linear growth in entanglement entropy (EE), indicating a heating phase with volume law entanglement. Surprisingly, for driving periods below a critical value T_ast, the EE grows subextensively with time, characteristic of a local quantum quench. In the non-interacting limit, we analytically trace the origin of this phenomenon to a transition in the single-particle Floquet quasi-energy spectrum. We also find that for T>T_*, the so-called "average energy" operator develops non-local, rainbow-like couplings that are responsible for the rapid entanglement growth in the heating phase, but remains local for T<T_*. Using extensive matrix-product-state simulations, we show that the non-heating phase and the subextensive entanglement growth persist in the presence of weak interactions for numerically accessible timescales. Our results establish that local Floquet engineering can generate emergent bulk phenomena, shedding new light on energy localization and thermalization in driven many-body systems.