  The two-dimensional Peierls-Hubbard model is studied at half-filling within
both Hartree-Fork and Kotliar-Ruckenstein slave-boson theory. The interplay
between two types of long-range order, bond-order wave (BOW) and
antiferromagnetism (AFM), is analysed for two representative dimerization
patterns, corresponding both to the same wavevector $(\pi,\pi)$. For each
pattern, the Peierls dimerization (and associated BOW) is weakened and finally
suppressed with increasing Hubbard on-site interaction, and correspondingly AFM
is gradually enhanced. In particular, a coexistence regime with both BOW and
AFM order is established in the parameter space of electron-lattice and Hubbard
interactions.
