  We present a numerical method to simulate the time evolution, according to a
Hamiltonian made of local interactions, of quantum spin chains and systems
alike. The efficiency of the scheme depends on the amount of the entanglement
involved in the simulated evolution. Numerical analysis indicate that this
method can be used, for instance, to efficiently compute time-dependent
properties of low-energy dynamics of sufficiently regular but otherwise
arbitrary one-dimensional quantum many-body systems.
