Dynamics of Rényi entanglement entropy in diffusive qudit systems

Abstract

Abstract My previous work [arXiv:1902.00977] studied the dynamics of Rényi entanglement entropy R α in local quantum circuits with charge conservation. Initializing the system in a random product state, it was proved that R α with Rényi index α > 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 ≥ 2 .