Using variational cluster perturbation theory we study the competition between $d$-wave superconductivity ($d\mathrm{SC}$) and antiferromagnetism (AF) in the $t\mathrm{\text{−}}{t}^{\prime }\mathrm{\text{−}}{t}^{\prime \prime }\mathrm{\text{−}}U$ Hubbard model. Large scale computer calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors as well as the one-particle excitation spectra for both hole and electron doping. We identify clear signatures of the Mott gap as well as of AF and of $d\mathrm{SC}$ that should be observable in photoemission experiments.

• Received 7 October 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.156404