  We show how to combine the light-cone and matrix product algorithms to
simulate quantum systems far from equilibrium for long times. For the case of
the XXZ spin chain at $\Delta=0.5$, we simulate to a time of $\approx 22.5$.
While part of the long simulation time is due to the use of the light-cone
method, we also describe a modification of the iTEBD algorithm with improved
numerical stability, and we describe how to incorporate symmetry into this
algorithm. While statistical sampling error means that we are not yet able to
make a definite statement, the behavior of the simulation at long times
indicates the appearance of either "revivals" in the order parameter as
predicted previously or of a distinct shoulder in the decay of the order
parameter.
