Dynamical Cluster Approximation

The dynamical cluster approximation (DCA) is a method which systematically incorporates nonlocal corrections to the dynamical mean-field approximation. Here we present a pedagogical discussion of the DCA by describing it as a ̊-derivable coarse-graining approximation in k-space, which maps an infinite lattice problem onto a periodic finite-sized cluster embedded in a self-consistently determined effective medium. We demonstrate the method by applying it to the two-dimensional Hubbard model. From this application, we show evidences of the presence of a quantum critical point (QCP) at a finite doping underneath the superconducting dome. The QCP is associated with the second-order terminus of a line of first order phase separation transitions. This critical point is driven to zero temperature by varying the band parameters, generating the QCP. The effect of the proximity of the QCP to the superconducting dome is also discussed.