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

TL;DR

This paper explores the nature of dynamical phase transitions by extending the survival amplitude into the complex time plane, revealing how zeros in this complex domain relate to non-analyticities in out-of-equilibrium quantum systems.

Contribution

It introduces the complex-time survival amplitude framework and demonstrates its application to the transverse-field Ising model, linking zeros in complex time to dynamical phase transitions.

Findings

Zeros of the complex-time survival amplitude indicate critical points.

The approach clarifies the role of excited-state quantum phase transitions.

Numerical analysis confirms the theoretical predictions.

Abstract

Dynamical phase transitions are defined through non-analyticities 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 non-analytical 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 changes is presented. The influence of the excited-state quantum phase transition is also put into context.