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 ‘‘off-diagonal’’ terms, not expressible purely in terms of site densities, representing bond-bond (W) 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 effects of the off-diagonal W and X terms on dimerization in the one-dimensional, half-filled-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 weak- and 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 (W,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of W 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 W. 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.