Abstract
We study exact zeros of Loschmidt echo and quantum speed limit time for dynamical quantum phase transition in finite size systems. Our results illustrate that exact zeros of Loschmidt echo exist even in finite size quantum systems when the postquench parameter takes some discrete values in regions with the corresponding equilibrium phase different from the initial phase. As the system size increases and tends to infinity, the discrete parameters distribute continuously in the parameter regions. We further analyze the time for the appearance of the first exact zero of Loschmidt echo which is known as the quantum speed limit time τ_QSL. We demonstrate that the maximal value of τ_QSL is proportional to L and approaches infinity in the thermodynamical limit, when we quench the initial non-critical state to the critical phase. We also calculate the minimal value of τ_QSL and find that its behavior is dependent on the phase of initial state.