  In this study, we explore the impact of short-range antiferromagnetic
correlations on the charge density wave (CDW) phase in strongly correlated
electron systems exhibiting the pseudogap phenomenon. Our investigation employs
a n-pole approximation to consider the repulsive Coulomb interaction $(U)$ and
antiferromagnetic correlations. Utilizing a two-dimensional Hubbard model for
the Coulomb interaction and a BCS-like model for the CDW order parameter, we
observe that an increase in $U$ enhances antiferromagnetic fluctuations,
resulting in a flattened re-normalized band around the anti-nodal point
$(\pi,0)$. The pseudogap manifests in the band structure and density of states,
prompting an exploration across various $U$ and occupation number values. Our
findings indicate that antiferromagnetic correlations significantly influence
the CDW state, as the Fermi surface is reconstructed within the ordered phase.
Furthermore, we find a Lifhsitz transition inside both the CDW phase and the
normal state, with the latter preceding the onset of the pseudogap.
