  Although most quantum systems thermalize locally on short time scales
independent of initial conditions, recent developments have shown this is not
always the case. Lattice geometry and quantum mechanics can conspire to produce
constrained quantum dynamics and associated glassy behavior, a phenomenon that
falls outside the rubric of the eigenstate thermalization hypothesis.
Constraints "fragment" the many-body Hilbert space due to which some states
remain insulated from others and the system fails to attain thermal
equilibrium. Such fragmentation is a hallmark of geometrically frustrated
magnets with low-energy "icelike manifolds" exhibiting a broad range of
relaxation times for different initial states. Focusing on the highly
frustrated kagome lattice, we demonstrate these phenomena in the
Balents-Fisher-Girvin Hamiltonian (easy-axis regime), and a three-coloring
model (easy-plane regime), both with constrained Hilbert spaces. We study their
level statistics and relaxation dynamics to develop a coherent picture of
fragmentation in various limits of the XXZ model on the kagome lattice.
