Modeling electron-electron interactions in reduced-dimensional materials: Bond-charge Coulomb repulsion and dimerization in Peierls-Hubbard models.

To the conventional Peierls-Hubbard model, involving both on-site ( U) and nearest-neighbor ( V) Coulomb repulsions, we add "o5'-diagonal" terms, not expressible purely in terms of site densities, representing bond-bond ( F) and mixed bond-site (X) electron-electron repulsive interactions involving nearest neighbors. We review earlier analyses of these interactions and discuss relative magnitudes of the parameters in applications to real materials. As a specific illustration, we investigate the e6'ects of the o8'-diagonal 8' and X terms on dimerization in the one-dimensional, halffilled-band Peierls-Hubbard models, which have been widely applied to conjugated polymers (such as trans-polyacetylene) and to related quasi-one-dimensional charge-density wave (CDW) systems. Using both weakand strong-coupling perturbation theory for large systems and exact diagonalizations of small systems, we investigate thoroughly the nature of the ground state of the model. For a broad range of the site-diagonal Hubbard parameters (U, V), including the values believed to be relevant to trans-polyacetylene, we find that the ofF-'diagonal terms (F,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of 8'relative to U and V, dimerization is destroyed, and the BOW ground state goes over to a ferromagnetic ground state or a CDW ground state, depending on the relative sizes of U, V, and 8'. We conclude with a general discussion of the applicability of the Peierls-Hubbard models to quasi-one-dimensional materials, including the potential importance of the breaking of charge conjugation ("particle-hole" ) symmetry by the X term.