A controlled route to the competing phases and the single-particle spectral function in the ground state of the 2D Hubbard model

Results are presented for the competition between d-wave superconductivity (dSC) and antiferromagnetism (AF) in the ground state of the two-dimensional (2D) Hubbard model, relevant for the high-Tc superconductors (HTSC). Using the variational cluster approach (VCA) we are able to resolve the low energy features at zero temperature and to calculate the spectral function for any wave vector in the Brillouin zone. The cluster calculations reproduce the overall ground-state phase diagram of the HTSC both for hole- and electron-doping. Consistent with experiments, the AF state is found to be significantly more robust for electron doping than for hole doping, resulting from the frustration induced by the next-nearest neighbor hopping in the Hubbard model. Moreover, the system shows a tendency to phase separation into a mixed AF-dSC phase at low and a pure dSC phase at higher doping, where the phase-separation energy is an order of magnitude larger for hole-doping.