Integrability breaking in the Rule 54 cellular automaton

TL;DR

This paper investigates how integrability breaking affects the Rule 54 cellular automaton, revealing the transition from integrable behavior to thermalization and diffusion, and calculating the resulting diffusion constant.

Contribution

It provides a perturbative analysis of integrability breaking in the Rule 54 automaton, connecting soliton backscattering to thermalization and transport properties.

Findings

Demonstrates onset of thermalization due to integrability breaking.

Calculates diffusion constant perturbatively.

Links soliton backscattering to transport coefficients.

Abstract

Cellular automata have recently attracted a lot of attention as testbeds to explore the emergence of many-body quantum chaos and hydrodynamics. We consider the Rule 54 model, one of the simplest interacting integrable models featuring two species of quasiparticles (solitons), in the presence of an integrability-breaking perturbation that allows solitons to backscatter. We study the onset of thermalization and diffusive hydrodynamics in this model, compute perturbatively the diffusion constant of tracer particles, and comment on its relation to transport coefficients.