Orthogonality catastrophe and quantum speed limit for dynamical quantum phase transition

We investigate the orthogonality catastrophe and quantum speed limit in the Creutz model for dynamical quantum phase transitions. We show that exact zeros of the Loschmidt echo can exist in finite-size systems for specific discrete values. We highlight the role of the zero-energy mode when analyzing quench dynamics near the critical point. Additionally, we examine the behaviors of the time for the first exact zeros of the Loschmidt echo and the corresponding quantum speed limit time as the system size increases. While the bound is not tight, it can be attributed to the scaling properties of the band gap and energy variance with respect to system size. As such, we establish a link between the orthogonality catastrophe and quantum speed limit by referencing the full form of the Loschmidt echo. In addition, we reveal the potential that the quantum speed limit holds to detect static quantum phase transition point and a reduced amplitude of the noise induced behaviors of quantum speed limit.