Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

Understand

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.