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arXiv · 2212.08028

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

Ángel L. Corps·Pavel Stránský·Pavel Cejnar
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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.

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Ángel L. Corps, Pavel Stránský, Pavel Cejnar. 2022-12-15. Mechanism of dynamical phase transitions: The complex-time survival amplitude. https://doi.org/10.1103/physrevb.107.094307

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