Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

TL;DR

This paper provides exact formulas for entanglement growth in the quantum cellular automaton Rule 54 after quantum quenches, confirming the quasiparticle picture for von Neumann entropy but not for other Re9nyi entropies.

Contribution

It introduces an exact analytical approach to entanglement dynamics in Rule 54, linking local relaxation to Gibbs states and validating the quasiparticle picture for von Neumann entropy.

Findings

Exact formulas for asymptotic linear growth of Re9nyi entropies.

Confirmation of the quasiparticle picture for von Neumann entropy.

No meaningful quasiparticle description for other Re9nyi entropies.

Abstract

We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule $54$. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all R\'enyi entropies in the thermodynamic limit and their eventual saturation for finite subsystems. While in the case of von Neumann entropy we recover exactly the predictions of the quasiparticle picture, we find no physically meaningful quasiparticle description for other R\'enyi entropies. Our results apply to both homogeneous and inhomogeneous quenches.