We present a determinant quantum Monte Carlo study of the competition between instantaneous on-site Coulomb repulsion and retarded phonon-mediated attraction between electrons, as described by the two dimensional Hubbard-Holstein model. At half filling, we find a strong competition between antiferromagnetism (AFM) and charge density wave (CDW) order. We demonstrate that a simple picture of AFM-CDW competition that incorporates the phonon mediated attraction into an effective-U Hubbard model requires significant refinement. Specifically, retardation effects slow the onset of charge order, so that CDW order remains absent even when the effective U is negative. This delay opens a window where neither AFM nor CDW order is well established, and where there are signatures of a possible metallic phase.
@article{arxiv.1209.0829,
title = {Competition between antiferromagnetic and charge density wave order in the half filled Hubbard-Holstein model},
author = {E. A. Nowadnick and S. Johnston and B. Moritz and R. T. Scalettar and T. P. Devereaux},
journal= {arXiv preprint arXiv:1209.0829},
year = {2015}
}