Antiferromagnetism and d-wave superconductivity in cuprates: A cluster dynamical mean-field theory

We present an approach to investigate the interplay of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model within a numerically exact cluster dynamical mean-field approximation. Self-consistent solutions with two nonzero order parameters exist in a wide range of doping level and temperatures. A linearized equation for the energy spectrum near the Fermi level has been solved. The resulting d-wave gap has the correct magnitude and k dependence, but some distortion compared to the pure $d_{x^2-y^2}$ superconducting order parameter due to the presence of underlying antiferromagnetic ordering.