Interplay between the charge density wave phase and a pseudogap under antiferromagnetic correlations

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.