Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators

TL;DR

This paper demonstrates that quench-induced dynamical quantum phase transitions can be detected through cusp singularities in expectation values and out-of-time-order correlators of quasilocal string operators, robust across models and initial states.

Contribution

It introduces a method to observe dynamical quantum phase transitions via string operator correlations, highlighting their robustness and sharpness with increasing string length.

Findings

Cusp singularities appear in string operator correlators after quenches.

Transitions are robust across different models and initial states.

Singularities become sharper with longer string operators.

Abstract

We analyze signatures of the dynamical quantum phase transitions in physical observables. In particular, we show that both the expectation value and various out of time order correlation functions of the finite length product or string operators develop cusp singularities following quench protocols, which become sharper and sharper as the string length increases. We illustrated our ideas analyzing both integrable and nonintegrable one-dimensional Ising models showing that these transitions are robust both to the details of the model and to the choice of the initial state.