  The widely used density matrix renormalization group (DRMG) method often
fails to converge in systems with multiple length scales, such as lattice
discretizations of continuum models and dilute or weakly doped lattice models.
The local optimization employed by DMRG to optimize the wave function is
ineffective in updating large-scale features. Here we present a multigrid
algorithm that solves these convergence problems by optimizing the wave
function at different spatial resolutions. We demonstrate its effectiveness by
simulating bosons in continuous space, and study non-adiabaticity when ramping
up the amplitude of an optical lattice. The algorithm can be generalized to
tensor network methods, and be combined with the contractor renormalization
group (CORE) method to study dilute and weakly doped lattice models.
