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We study the ground state properties of the Holstein-Hubbard model on some bipartite lattices at half-filling; The ground state is proved to exhibit ferrimagnetism whenever the electron-phonon interaction is not so strong. In addition, the antiferromagnetic long-range order is shown to exist in the ground state. In contrast to this, we prove the absence of the long-range charge order. [ABSTRACT FROM AUTHOR]

The Holstein model has widely been 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. [ABSTRACT FROM AUTHOR]

Ground state properties of the SSH model are studied. In particular, the uniqueness of the ground state is proven. As a consequence, characteristic spin structure of the ground state is revealed. [ABSTRACT FROM AUTHOR]

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit α → 0 together with the relative distance between the atoms increasing as α-γR, γ > 0. In particular we determine explicitly the crossover function from the R-6 van der Waals potential to the R-7 retarded van der Waals potential, which takes place at scale α-2R. [ABSTRACT FROM AUTHOR]