Missing bond-charge repulsion in the extended Hubbard model: Effects in polyacetylene

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Abstract
Translational invariance requires that the electron density operator is not diagonal in a Wannier representation. We show that this leads to important terms in the electron-electron interaction Hamiltonian, terms which involve the bond-charge density and which are not included in the widely studied extended Hubbard model. When these bond-charge interactions are included, we find that electron-electron repulsion tends to stiffen the lattice (for physically reasonable parameters) and to oppose dimerization in polyacetylene and in other charge-density-wave systems. A related decrease in the Peierls gap for fixed dimerization is also obtained. These conclusions are in contrast with previous results obtained from the extended Hubbard model.