Abstract
Dynamical phase transitions are defined through nonanalyticities of the survival probability of an out-of-equilibrium time-evolving state at certain critical times. They ensue from zeros of the corresponding survival amplitude.
By extending the time variable onto the complex domain, we formulate the complex-time survival amplitude. The complex zeros of this quantity near the time axis correspond, in the infinite-size limit, to nonanalytical points where the survival probability abruptly vanishes.
Our results are numerically exemplified in the fully connected transverse-field Ising model, which displays a symmetry-broken phase delimited by an excited-state quantum phase transition. A detailed study of the behavior of the complex-time survival amplitude when the characteristics of the out-of-equilibrium protocol change is presented.
The influence of the excited-state quantum phase transition is also put into context.