Numerical Computation of Dynamically Important Excited States of Many-Body Systems

We present an extension of the time-dependent Density Matrix Renormalization Group (t-DMRG), also known as Time Evolving Block Decimation algorithm (TEBD), allowing for the computation of dynamically important excited states of one-dimensional many-body systems. We show its practical use for analyzing the dynamical properties and excitations of the Bose-Hubbard model describing ultracold atoms loaded in an optical lattice from a Bose-Einstein condensate. This allows for a deeper understanding of nonadiabaticity in experimental realizations of insulating phases.