Comment on "Entanglement growth in diffusive systems"

TL;DR

This paper critiques a recent claim about entanglement growth in diffusive systems, showing that sub-ballistic growth conditions are more broadly applicable across various models and dimensions.

Contribution

It broadens the understanding of conditions for sub-ballistic entanglement growth, extending applicability beyond specific models to more general systems.

Findings

Sub-ballistic growth conditions are more general than previously thought.

Applicable to systems with larger local Hilbert spaces and in arbitrary dimensions.

Challenges previous assumptions about entanglement growth in diffusive systems.

Abstract

In a recent paper (Commun. Phys. 3, 100) Znidaric studies the growth of higher Renyi entropies in diffusive systems and claims that they generically grow ballistically in time, except for spin-1/2 models in d=1 dimension. Here, we point out that the necessary conditions for sub-ballistic growth of Renyi entropies are in fact much more general, and apply to a large class of systems, including experimentally relevant ones in arbitrary dimension and with larger local Hilbert spaces.