Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

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 Rényi 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 Rényi entropies. Our results apply to both homogeneous and inhomogeneous quenches.

Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems

“…Our ability to compute R 2 (t) has given us insight into equilibration times in the coupled Luttinger liquid, the importance of the GGE for describing the post-quench dynamics, as well as the importance of the role of higher order breather states that arise because of the non-linear cosine interaction term. We mention that while the quasiparticle picture [58] provides the exact time evolution of the von Neumann entropy (n = 1) for arbitrary integrable models [59,60], the same is not true [61][62][63][64] for the experimentally accessible Renyi entropies for which our approach is the only viable methodology for both integrable and chaotic post-quench dynamics. R.M.K.…”

Integrable spin chains and cellular automata with medium range interaction

“…The most important example is the Rule54 model, which is often called the simplest interacting integrable model [70]. It is a very special model with soliton-like behaviour, which allows for exact solutions [71][72][73] and integrable quantum deformations [74] (see also [75]). However, the connection with the standard Yang-Baxter integrability remained unknown.…”

Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps

“…BCA with Floquet type update rules attracted considerable attention in the last couple of years, both with finite and continuous configuration spaces [23,24]. In the finite case the most studied system has been the so-called Rule54 model [8,25,7], where exact solutions were found for the dynamics despite the model being interacting [26,27,28,29]. Quite surprisingly, despite having perhaps the simplest dynamics among interacting models, the algebraic integrability of the Rule54 model is still not clarified, see [30,31].…”