Pseudogap to metal transition in the anisotropic two-dimensional Hubbard model

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 $t_y/t_x\sim 0.5$.