Time evolution of matrix product states

Abstract

In this work, we develop several new simulation algorithms for one-dimensional (1D) many-body quantum mechanical systems combining the Matrix Product State variational ansatz (vMPS) with Taylor, Padé and Arnoldi approximations to the evolution operator. By comparing with previous techniques based on vMPS and Density Matrix Renormalization Group (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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.