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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.
Kivelson et al. (Mon,) studied this question.