Time evolution of one-dimensional quantum many body systems

The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one-dimensional systems. We describe recent developments in the construction of numerical schemes for general (one-dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest-neighbor-interaction and investigate their accuracy by comparing with exact results.