A Yang-Baxter integrable cellular automaton with a four site update rule

TL;DR

This paper introduces a new Yang-Baxter integrable cellular automaton with a four-site update rule, exhibiting rich dynamics including stable particles and factorized multi-particle scattering, and proves its integrability through transfer matrices and a novel Lax operator.

Contribution

The paper constructs a Yang-Baxter integrable cellular automaton with a four-site update rule and introduces a new Lax operator, advancing the understanding of integrable models in cellular automata.

Findings

Model exhibits three types of stable particles.

Multi-particle scattering is factorized.

Existence of commuting transfer matrices proven.

Abstract

We present a one dimensional reversible block cellular automaton, where the time evolution is dictated by a period 3 cycle of update rules. At each time step a subset of the cells is updated using a four site rule with two control bits and two action bits. The model displays rich dynamics. There are three types of stable particles, left movers, right movers and "frozen" bound states that only move as an effect of scattering with the left and right movers. Multi-particle scattering in the system is factorized. We embed the model into the canonical framework of Yang-Baxter integrability by rigorously proving the existence of a commuting set of diagonal-to-diagonal transfer matrices. The construction involves a new type of Lax operator.