  The two-dimensional Hubbard model on the square lattice is studied in the
presence of lattice distortions in the adiabatic approximation. The self energy
is computed within perturbation theory up to second order, which provides a way
for studying the quasiparticle dispersion. We compute numerically the second
order contribution to the self-energy using a standard Fast Fourier Transform
Algorithm for finite system sizes. The stability of the lattice distortions is
investigated and a schematic phase diagram is drawn. The Fermi surface is
analyzed for densities near to half filling, the presence of lattice distortion
change some spectral properties of the model and gives an anisotropic
interacting FS. The spectral function is calculated along several lines in
momentum space and the renormalized quasiparticle dispersion is obtained. The
behavior of the density of states is shown for different values of the
intrasite repulsion U in the different phases.
