Subdiffusive transport in the Fredkin dynamical universality class

Fredkin-type kinetic constraints appear in systems ranging from classical interfaces to th e Fredkin and Motzkin quantum spin chains. Here, we identify a pseudolocal conserved charge associated with Fredkin-constrained dynamics that may be leveraged to subdiffusively bound the dynamical exponent $z\ensuremath{\ge}5/2$. Our results establish that transport in Fredkin-constrained systems belongs to a distinct dynamical universality class that is separate from ordinary diffusion. This universality class is stable to local perturbations that conserve the pseudolocal charge.