The Holstein model has been widely accepted as a model comprising electrons
interacting with phonons; analysis of this model's ground states was
accomplished two decades ago. However, the results were obtained without
completely taking repulsive Coulomb interactions into account. Recent progress
has made it possible to treat such interactions rigorously; in this paper, we
study the Holstein--Hubbard model with repulsive Coulomb interactions. The
ground state properties of the model are investigated; in particular, the
ground state of the Hamiltonian is proven to be unique for an even number of
electrons on a bipartite connected lattice. In addition, we provide a rigorous
upper bound on charge susceptibility.Comment: 42 pages, Title changed, Major improvements, to appear, Annales Henri
Poincar
