Density Matrix Renormalization Group study of the polaron problem in the Holstein model

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 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 oneand 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 20×20 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. 71.38.+i Typeset using REVTEX