# Time dependence of entanglement entropy on the fuzzy sphere

## TL;DR

This study investigates how entanglement entropy evolves over time on a fuzzy sphere after a mass quench, revealing both ballistic spread consistent with local theories and faster-than-light spread in certain non-local regimes.

## Contribution

It provides the first numerical analysis of entanglement dynamics on a fuzzy sphere, highlighting the effects of non-locality on entanglement propagation.

## Key findings

- Entanglement spreads ballistically at or below the speed of light.
- In certain regimes, entanglement spreads faster than local models predict.
- Pre-quench mass influences the speed and nature of entanglement propagation.

## Abstract

We numerically study the behaviour of entanglement entropy for a free scalar field on the noncommutative ("fuzzy") sphere after a mass quench. It is known that the entanglement entropy before a quench violates the usual area law due to the non-local nature of the theory. By comparing our results to the ordinary sphere, we find results that, despite this non-locality, are compatible with entanglement being spread by ballistic propagation of entangled quasi-particles at a speed no greater than the speed of light. However, we also find that, when the pre-quench mass is much larger than the inverse of the short-distance cutoff of the fuzzy sphere (a regime with no commutative analogue), the entanglement entropy spreads faster than allowed by a local model.