Time evolution algorithms for Matrix Product States and DMRG

In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator. By comparing with previous techniques based on MPS and DMRG we demonstrate that the Arnoldi method is the best one, reaching extremely good accuracy with moderate resources. Finally we apply this algorithm to studying how correlations are transferred from the atomic to the molecular cloud when crossing a Feschbach resonance with two-species hard-core bosons in a 1D optical lattice.