# Dynamics of Renyi entanglement entropy in local quantum circuits with charge conservation

## TL;DR

This paper investigates the growth of Renyi entanglement entropy in charge-conserving quantum circuits, proving an upper bound under diffusive charge transport and confirming it with recent numerical results.

## Contribution

The paper provides a rigorous proof of the upper bound on Renyi entanglement entropy growth and connects it with recent numerical findings in charge-conserving quantum circuits.

## Key findings

- Renyi entanglement entropy with index > 1 grows at most as O(√t ln t) under diffusive charge transport.
- Recent numerical simulations show this bound is nearly saturated in random local quantum circuits.
- The work links entanglement dynamics with charge transport properties in quantum circuits.

## Abstract

In local quantum circuits with charge conservation, we initialize the system in random product states and study the dynamics of the Renyi entanglement entropy $R_\alpha$. We rigorously prove that $R_\alpha$ with Renyi index $\alpha>1$ at time $t$ is $\le O(\sqrt{t\ln t})$ if the transport of charges is diffusive. Very recent numerical results of Rakovszky et al. show that this upper bound is saturated (up to the sub-logarithmic correction) in random local quantum circuits with charge conservation.