Subdiffusive transport in the Fredkin dynamical universality class

We identify a pseudolocal conserved charge in the Fredkin and Motzkin quantum spin chains and explore its consequences for the hydrodynamics of systems with Fredkin- or Motzkin-type kinetic constraints. We use this quantity to formulate an exact upper bound $\mathcal{O}(L^{-5\mathrm{/}2})$ on the gap of the Fredkin and Motzkin spin chains. Our results establish that transport in kinetically constrained dynamical systems with Fredkin or Motzkin constraints is subdiffusive, with dynamical exponent $z\ge 5\mathrm{/}2$.