  The transition between a metallic and a pseudogap phase in high-$T_c$ cuprate
superconductors is the subject of experimental investigations but has not been
settled theoretically, even within the context of the Hubbard model. We apply
the Cluster Dynamical Impurity Approximation (CDIA) to the anisotropic Hubbard
model on the square lattice at zero temperature and finite doping. This
approach can detect a first-order transition between two metallic states: a
pseudogap state at low doping, with a depleted density of states at the Fermi
level, and a correlated metal at higher doping. This transition was first seen
in Cluster dynamical mean field theory at finite temperature by Sordi et al on
the isotropic Hubbard model. Here we investigate this transition at zero
temperature and a as function of on-site interaction $U$, anisotropy $t_y/t_x$
and doping. We find a first-order transition line which ends at a quantum
critical point, which occurs around $t_y/t_x\sim 0.5$.
