  We study the dynamics of a single excitation in an infinite XXZ spin chain,
which is launched from the origin. We study the time evolution of the spread of
entanglement in the spin chain and obtain an expression for the second order
spatial moment of concurrence, about the origin, for both ordered and
disordered chains. In this way, we show that a finite central disordered region
can lead to sustained superballistic growth in the second order spatial moment
of entanglement within the chain.
