We present a method for solving impurity models with electron-phonon coupling, which treats the phonons efficiently and without approximations. The algorithm is applied to the Holstein-Hubbard model in the dynamical mean field approximation, where it allows access to strong interactions, very low temperatures and arbitrary fillings. We show that a renormalized Migdal-Eliashberg theory provides a reasonlable description of the phonon contribution to the electronic self energy in strongly doped systems, but fails if the quasiparticle energy becomes of order of the phonon frequency.
@article{arxiv.cond-mat/0701730,
title = {Efficient DMFT-simulation of the Holstein-Hubbard Model},
author = {Philipp Werner and Andrew J. Millis},
journal= {arXiv preprint arXiv:cond-mat/0701730},
year = {2009}
}