Real space thermalization of locally driven quantum magnets

The study of thermalization and its breakdown in isolated systems has led to a deeper understanding of non-equilibrium quantum states and their dependence on initial conditions. The role of initial conditions is prominently highlighted by the existence of quantum many-body scars, special athermal states with an underlying effective superspin structure, embedded in an otherwise chaotic many-body spectrum. Spin Heisenberg and $XXZ$ models and their variants in one and higher dimension have been shown to host exact quantum many-body scars, exhibiting perfect revivals of spin helix states that are realizable in synthetic and condensed matter systems. Motivated by these advances, we propose experimentally accessible, local, time-dependent protocols to explore the spatial thermalization profile and highlight how different parts of the system thermalize and affect the fate of the superspin. We identify distinct parametric regimes for the ferromagnetic ($X$-polarized) initial state based on the interplay between the driven spin and the rest, including local athermal behavior where the driven spin effectively decouples, acting like a ``cold" spot while being instrumental in heating up the other spins. We also identify parameter regimes where the superspin remains resilient to local driving for long time scales. We develop a real and Floquet space picture that explains our numerical observations, and make predictions that can be tested in various experimental setups.