Spread Complexity in free fermion models

We study spread complexity and the statistics of work done for quenches in the three-spin interacting Ising model, the XY spin chain, and the Su-Schrieffer-Heeger model. We study these models without quench and for different schemes of quenches, such as sudden quench and multiple sudden quenches. We employ the Floquet operator technique to investigate all three models in the presence of time-dependent periodic driving of parameters. In contrast to the sudden quenched cases, the periodically varying parameter case clearly shows non-analytical behaviour near the critical point. We also elucidate the relation between work done and the Lanczos coefficient and how the statistics of work done behave near critical points.