Dynamics of Rényi entanglement entropy in diffusive qudit systems

Abstract

My previous work [arXiv:1902.00977] studied the dynamics of Rényi entanglement entropy $R_{\hat{I}}\pm$ in local quantum circuits with charge conservation. Initializing the system in a random product state, it was proved that $R_{\hat{I}}\pm$ with Rényi index $\hat{I}\pm >1$ grows no faster than "diffusively" (up to a sublogarithmic correction) if charge transport is not faster than diffusive. The proof was given only for qubit or spin-$1/2$ systems. In this note, I extend the proof to qudit systems, i.e., spin systems with local dimension $d\ge 2$.

v2: title changed and abstract expanded