  We investigate the equilibration dynamics of string order in one-dimensional
quantum systems. After initializing a spin-1 chain in the Haldane phase, the
time evolution of non-local correlations following a sudden quench is studied
by means of matrix-product-state-based algorithms. Thermalization occurs only
for scales up to a horizon growing at a well defined speed, due to the finite
maximal velocity at which string correlations can propagate, related to a
Lieb-Robinson bound. The persistence of string ordering at finite times is
non-trivially related to symmetries of the quenched Hamiltonian. A
qualitatively similar behavior is found for the string order of the Mott
insulating phase in the Bose-Hubbard chain. This paves the way towards an
experimental testing of our results in present cold-atom setups.
