Exact solution of the Rule 150 reversible cellular automaton

Understand

We study the dynamics of the Rule 150 reversible cellular automaton (RCA).

• This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics, corresponding to a bulk deterministic and reversible discrete version of the kinetically constrained XOR-Fredrickson-Andersen model, whereby the local dynamics is restricted: a site flips if and only if the states of its neighbouring sites are different from each other.
• Like other RCA which have been studied recently, such as Rule 54 and Rule 201, Rule 150 is integrable, however, in contrast is noninteracting.
• In particular, the emergent quasiparticles - the domain walls - behave as free fermions.