Many-body chaos and energy dynamics in holography

TL;DR

This paper demonstrates that pole-skipping, a signature of quantum chaos in energy density correlations, is a universal feature in holographic systems dual to Einstein gravity, revealing deep connections between chaos and energy dynamics.

Contribution

It shows the universality of pole-skipping in finite temperature holographic systems and uncovers a universal aspect of Einstein equations near black holes.

Findings

Pole-skipping is universal in Einstein gravity duals.

Analytic verification in a holographic axion model.

Universal features of Einstein equations around black holes.

Abstract

Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. The manifestation, referred to as pole-skipping, concerns the analytic behaviour of energy density two-point functions around a special point $\omega = i \lambda$, $k = i \lambda/v_B$ in the complex frequency and momentum plane. Here $\lambda$ and $v_B$ are the Lyapunov exponent and butterfly velocity characterising quantum chaos. In this paper we provide an argument that the phenomenon of pole-skipping is universal for general finite temperature systems dual to Einstein gravity coupled to matter. In doing so we uncover a surprising universal feature of the linearised Einstein equations around a static black hole geometry. We also study analytically a holographic axion model where all of the features of our general argument as well as the pole-skipping phenomenon can be verified in detail.