Entanglement wedge method, out-of-time-ordered correlators, and pole skipping

TL;DR

This paper compares three methods—entanglement wedge, out-of-time-ordered correlators, and pole-skipping—to analyze chaos in Lifshitz black holes, finding they produce consistent results for Lyapunov exponent and butterfly velocity, and explores classical and quantum aspects of chaos.

Contribution

It demonstrates the equivalence of three different methods in probing chaos in Lifshitz black holes and discusses classical and quantum perspectives on chaotic properties.

Findings

All methods yield identical butterfly velocity and Lyapunov exponent.

Chaotic properties depend nontrivially on anisotropy index.

Classical eikonal phase reveals different scattering regimes near horizon and boundary.

Abstract

We investigate two salient chaotic features, namely Lyapunov exponent and butterfly velocity, for an asymptotically Lifshitz black hole background with arbitrary dynamical critical exponent. These features are computed using three methods: entanglement wedge method, out-of-time-ordered correlator computation and pole-skipping. We present a comparative study where all of these methods yield exactly similar results for the butterfly velocity and Lyapunov exponent. This establishes an equivalence between all three methods for probing chaos in the chosen gravity background. Furthermore, we evaluate the chaos at the classical level by computing the eikonal phase and Lyapunov exponent from the bulk gravity. In the classical approach, we comment on potential limitations while choosing the turning point of the null geodesic in our gravity background. All chaotic properties emerge as nontrivial functions of the anisotropy index. By examining the classical eikonal phase, we uncover different scattering scenarios in the near-horizon and near-boundary regimes. Finally, we remark on a possible classical/quantum correspondence from the analysis of classical eikonal phase shift and Lyapunov exponent.