Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field

TL;DR

This paper explores how pole-skipping points in holographic models relate to chaos and diffusion bounds, revealing a universal connection between symmetry breaking, chaos parameters, and diffusion constants.

Contribution

It demonstrates that the diffusion constant is bounded by chaos parameters regardless of explicit or spontaneous symmetry breaking, confirmed through pole-skipping analysis.

Findings

Diffusion constant bounded by chaos parameters ($v_B^2/\lambda_L$).

Pole-skipping points relate to chaos properties independently of symmetry breaking.

Lower bound on diffusion constant confirmed in low temperature limit.

Abstract

We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent ($\lambda_L$) and butterfly velocity ($v_B$), independently of the symmetry breaking patterns. We show that the diffusion constant ($D$) is bounded by $D \,\geqslant\, v_{B}^2/\lambda_{L}$, where $D$ is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.