  Using the variational cluster approach (VCA), we study the transition from
the antiferromagnetic to the superconducting phase of the two-dimensional
Hubbard model at zero temperature. Our calculations are based on a new method
to evaluate the VCA grand potential which employs a modified Lanczos algorithm
and avoids integrations over the real or imaginary frequency axis. Thereby,
very accurate results are possible for cluster sizes not accessible to full
diagonalization. This is important for an improved treatment of short-range
correlations, including correlations between Cooper pairs in particular. We
investigate the cluster-size dependence of the phase-separation tendency that
has been proposed recently on the basis of calculations for smaller clusters.
It is shown that the energy barrier driving the phase separation decreases with
increasing cluster size. This supports the conjecture that the ground state
exhibits microscopic inhomogeneities rather than macroscopic phase separation.
The evolution of the single-particle spectum as a function of doping is studied
in addtion and the relevance of our results for experimental findings is
pointed out.
