  Atypical eigenstates in the form of quantum scars and fragmentation of
Hilbert space due to conservation laws provide obstructions to thermalization
in the absence of disorder. In certain models with dipole and $U(1)$
conservation, the fragmentation results in subdiffusive transport. In this
paper we study the interplay between scarring and weak fragmentation giving
rise to anomalous hydrodynamics in a class of one-dimensional spin-$1$
frustration-free projector Hamiltonians, known as deformed Motzkin chain. The
ground states and low-lying excitations of these chains exhibit large
entanglement and critical slowdown. We show that at high energies the
particular form of the projectors causes the emergence of disjoint Krylov
subspaces for open boundary conditions, with an exact quantum scar being
embedded in each subspace, leading to slow growth of entanglement and localized
dynamics for specific out-of-equilibrium initial states. Furthermore, focusing
on infinite temperature, we unveil that spin transport is subdiffusive, which
we corroborate by simulations of constrained stochastic cellular automaton
circuits. Compared to dipole moment conserving systems, the deformed Motzkin
chain appears to belong to a different universality class with distinct
dynamical transport exponent and only polynomially many Krylov subspaces.

Statistical Mechanics;Quantum Physics