Dynamical quantum phase transitions and quantum speed limit time in finite-size XY chain coupled by a central spin

Based on the finite-size XY chain coupled by a single-spin system, we study the exact zeros of the Loschmidt echo and the quantum speed limit (QSL) time during dynamical quantum phase transitions (DQPTs) driven by the anisotropy parameter and the external magnetic field. Two constraint relations satisfied by the quench parameters to ensure the exact zeros of the Loschmidt echo are obtained. Our results illustrate that DQPTs can still occur as the quench parameters do not cross the critical points where the perturbative effects of the central spin system play a decisive role. We demonstrate that the scaling behaviors of the QSL time (including maximal and minimal values) strongly depend on the anisotropy parameter, and are immune to perturbation of the coupled system.