Mechanism of dynamical phase transitions: The complex-time survival amplitude

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.

Automated summary

Dynamical phase transitions are defined by the nonanalytic behavior of the survival probability at certain critical times, which originate from the zeros of the survival amplitude. We introduce the complex-time survival amplitude by extending the time variable onto the complex domain, where the complex zeros near the time axis correspond to nonanalytic points where the survival probability abruptly vanishes in the infinite-size limit. We illustrate our results numerically in the fully connected transverse-field Ising model, which exhibits a symmetry-broken phase delimited by an excited-state quantum phase transition, and explore the behavior of the complex-time survival amplitude under changes in the out-of-equilibrium protocol, as well as the influence of the excited-state quantum phase transition.