Abstract
Some of the essential aspects of the propagation of electrons in solids are modelled by the simple Holstein-Hubbard model. It is a one band model that involves schematically the basic interactions between the electrons and the lattice. The Coulomb interactions of the electrons with the ions of the lattice are represented by linear on-site electron phonon couplings while the direct Coulomb electron-electron interactions are represented only by their local component as on-site Hubbard repulsions. The direct interactions between the ions of the lattice, including their Coulomb interactions, are represented phenomenologically by an elastic deformation potential.
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