  We propose a new density matrix renormalization group (DMRG) approach to
study lattices including bosons. The key to the new approach is an exact
mapping of a boson site containing 2^N states to N pseudo-sites, each with 2
states. The pseudo-sites can be viewed as the binary digits of a boson level.
We apply the pseudo-site DMRG method to the polaron problem in the one- and
two-dimensional Holstein models. Ground state results are presented for a wide
range of electron-phonon coupling strengths and phonon frequencies on lattices
large enough (up to 80 sites in one dimension and up to 20x20 sites in two
dimensions) to eliminate finite size effects, with up to 128 phonon states per
phonon mode. We find a smooth but quite abrupt crossover from a quasi-free
electron ground state with a slightly renormalized mass at weak electron-phonon
coupling to a polaronic ground state with a large effective mass at strong
coupling, in agreement with previous studies.
