Phase diagram of the Hubbard model: Beyond the dynamical mean field

The Dynamical Cluster Approximation (DCA) is used to study non-local corrections to the dynamical mean-field phase diagram of the two-dimensional Hubbard model. Regions of antiferromagnetic, d-wave superconducting, pseudo-gapped non-Fermi liquid, and Fermi liquid behaviors are found, in rough agreement with the generic phase diagram of the cuprates. The non-local fluctuations beyond the mean field both suppress the antiferromagnetism and mediate the superconductivity.