Dynamics of R\'enyi entanglement entropy in diffusive qudit systems

TL;DR

This paper extends previous results on the growth of Re9nyi entanglement entropy in local quantum circuits from qubit systems to qudit systems with local dimension db2, demonstrating similar diffusive bounds.

Contribution

It generalizes the proof of diffusive growth bounds of Re9nyi entanglement entropy to qudit systems, expanding applicability beyond spin-1/2 models.

Findings

Re9nyi entanglement entropy grows at most diffusively in qudit systems

The proof method is extended from qubit to higher local dimension systems

Supports the universality of diffusive entanglement growth in local quantum circuits

Abstract

My previous work [arXiv:1902.00977] studied the dynamics of R\'enyi entanglement entropy $R_\alpha$ in local quantum circuits with charge conservation. Initializing the system in a random product state, it was proved that $R_\alpha$ with R\'enyi index $\alpha>1$ 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 $d\ge2$.