We have made a few supplemental calculations to our original article [Phys. Rev. B 37, 9546 (1988)]. The energy crossover between ($\pi , 0$) and ($\pi , \pi$) phonons in the two-dimensional half-filled Hubbard model is shown to occur also on a 4×2 lattice for small lattice distortion. We also discuss further the effect of the on-site repulsion on the dimerization in the small-$U$ limit.

• Received 30 January 1989

DOI:https://doi.org/10.1103/PhysRevB.39.12327