  The effect of the electron-electron (e-e) interaction on the Peierls lattice
distortions due to the electron-lattice (e-l) interaction is studied in the
two-dimensional Peierls-Hubbard model, treating the fluctuation of e-e
interaction around the Hartree-Fock solution within the 2nd order perturbation
theory. In our previous work, using the Hartree-Fock approximation, we found
multimode Peierls lattice distortions with wave vectors, the nesting vector
$\mathbf{Q}$ and those parallel to it, are not affected by an e-e interaction
if it is weak compared with the e-l coupling. The phase transition between the
BOW (bond order wave) with multimode lattice distortions and the SDW (spin
density wave) with the wave vector $\mathbf{Q}$ behaves as the 1st order
transition. The property of the multimode BOW is found to change drastically
when we consider the fluctuation effect within the 2nd order perturbation
theory. The Fourier components of the multimode BOW increase gradually as the
e-e interaction parameter is increased. Especially the Fourier component with
the wave vector equal to the smallest reciprocal lattice vector in the presence
of the multimode BOW is most strongly affected by the fluctuation effect.
