  In the framework of cluster perturbation theory for the 2D Hubbard and
Hubbard-Holstein models at low hole doping we have studied the effect of local
and short-range correlations in strongly correlated systems on the anomalous
features in the electronic spectrum by investigating the fine structure of
quasiparticle bands. Different anomalous features of spectrum are obtained as
the result of intrinsic properties of strongly correlated electron and polaron
bands in the presence of short-range correlations. Particularly, features
similar to the electron-like Fermi-pockets of cuprates at hole doping
$p\sim0.1$ are obtained without ad hoc introducing a charge density wave order
parameter within the Hubbard model in a unified manner with other known
peculiarities of the pseudogap phase like Fermi-arcs, pockets, waterfalls, and
kink-like features. The Fermi surface is mainly formed by dispersive
quasiparticle bands with large spectral weight, formed by coherent low-energy
exications. Within the Hubbard-Holstein model at moderate phonon frequencies we
show that modest values of local electron-phonon interaction are capable of
introducing low-energy kink-like features and affecting the Fermi surface by
hybridization of the fermionic quasiparticle bands with the Franck-Condon
resonances.
