Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators

TL;DR

This paper demonstrates that out-of-time-ordered correlators can effectively detect both equilibrium and dynamical quantum phase transitions in various Ising chain models, including long-range and non-integrable variants.

Contribution

It introduces a method using OTO correlators to identify phase transitions in Ising chains, applicable to both equilibrium states and post-quench dynamics, including long-range interactions.

Findings

OTOC correlators detect quantum phase transitions in ground states.

Post-quench OTO correlators signal equilibrium critical points and phases.

Long-range models exhibit dynamical quantum phase transitions detectable by OTO correlators.

Abstract

Out-of-time-ordered (OTO) correlators have developed into a central concept quantifying quantum information transport, information scrambling and quantum chaos. In this work we show that such OTO correlator can also be used to dynamically detect equilibrium as well as nonequilibrium phase transitions in Ising chains. We study OTO correlators of an order parameter both in equilibrium and after a quantum quench for different variants of transverse-field Ising models in one dimension, including the integrable one as well as non-integrable and long-range extensions. We find for all the studied models that the OTO correlator in ground states detects the quantum phase transition. After a quantum quench from a fully polarized state we observe numerically for the short-range models that the asymptotic long-time value of the OTO correlator signals still the equilibrium critical points and ordered phases. For the long-range extension, the OTO correlator instead determines a dynamical quantum phase transition in the model. We discuss how our findings can be observed in current experiments of trapped ions or Rydberg atoms.