Charge diffusion and the butterfly effect in striped holographic matter

TL;DR

This paper analytically investigates charge diffusion and butterfly velocity in holographic matter with disorder, revealing that butterfly velocity does not impose a strict lower bound on charge diffusion in this context.

Contribution

It provides an analytical calculation of charge diffusion and butterfly velocity in a specific holographic model with disorder, challenging previous assumptions about bounds.

Findings

Butterfly velocity does not set a sharp lower bound for charge diffusion.

Analytical expressions for charge diffusion constant and butterfly velocity in the model.

Disorder in a single spatial direction affects the relation between diffusion and butterfly velocity.

Abstract

Recently, it has been proposed that the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals. We analytically compute the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength "hydrodynamic" disorder in a single spatial direction. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.