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 all methods with previous techniques based on Trotter decompositions we demonstrate that the Arnoldi method is the best one, reaching extremely good accuracy with moderate resources. Finally we apply this algorithm to studying the formation of molecules in an optical lattices when crossing a Feschbach resonance with a cloud of two-species hard-core bosons.
@article{arxiv.cond-mat/0602305,
title = {Time evolution of Matrix Product States},
author = {Juan Jose Garcia-Ripoll},
journal= {arXiv preprint arXiv:cond-mat/0602305},
year = {2007}
}
Comments
More extensive comparison with all nearest-neighbor spin s=1/2 models. The results in this manuscript have been superseded by a more complete work in cond-mat/0610210