Floquet dynamical quantum phase transitions in periodically flux-quenched systems

Floquet dynamical quantum phase transitions (FDQPTs) reveal many nonequilibrium critical phenomena in periodically driven quantum systems, and their underlying mechanisms have attracted deep attention in recent years. In this paper, we consider an extended XY spin chain under a periodic flux-quench protocol, and demonstrate the effect of the flux difference within each micromotion period on the emergence of FDQPTs, by analyzing physical quantities such as the Loschmidt echo, rate function, and dynamical topological order parameter (DTOP), etc. We also generalize the concept of quench fidelity to periodically driven systems, i.e., Floquet quench fidelity, and discuss the necessary and sufficient conditions for FDQPTs. In contrast to conventional single-quench scenarios, the occurrence of FDQPTs is determined by the requirement of Floquet quench fidelity condition and segment duration. Our framework may be applied generally to arbitrary periodically driven parameters, providing fundamental insights into how periodic protocols control nonequilibrium phase transitions in quantum many-body systems.