Exact solution of the Floquet-PXP cellular automaton

TL;DR

This paper presents an exact solution for a deterministic Floquet cellular automaton, revealing ballistic quasiparticle propagation and providing a matrix product state description of its stationary states, highlighting its integrability.

Contribution

It introduces an exact solution for the Floquet-PXP cellular automaton, including its stationary states and quasiparticle dynamics, demonstrating its integrability and broad boundary condition applicability.

Findings

Ballistic propagation of quasiparticles observed

Exact matrix product state form derived for stationary states

Model exhibits integrability and reversible dynamics

Abstract

We study the dynamics of a bulk deterministic Floquet model, the Rule 201 synchronous one-dimensional reversible cellular automaton (RCA201). The system corresponds to a deterministic, reversible, and discrete version of the PXP model, whereby a site flips only if both its nearest neighbours are unexcited. We show that the RCA201/Floquet-PXP model exhibits ballistic propagation of interacting quasiparticles - or solitons - corresponding to the domain walls between non-trivial three-fold vacuum states. Starting from the quasiparticle picture, we find the exact matrix product state form of the non-equilibrium stationary state for a range of boundary conditions, including both periodic and stochastic. We discuss further implications of the integrability of the model.