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, which is the subject of recent experimental investigations, is studied theoretically within the Hubbard model. We apply the cluster dynamical impurity approximation 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 seen first in the cluster dynamical mean-field theory at finite temperatures by Sordi et al. [Phys. Rev. Lett. 108, 216401 (2012)] on the isotropic Hubbard model. Here we investigate this transition at zero temperature and as a function of on-site interaction $U$, anisotropy ${t}_y/{t}_x$, and doping. We find a first-order transition line which ends at a critical point, which occurs around ${t}_y/{t}_x\ensuremath{\sim}0.5$.