Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects

Using the variational cluster approach, 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 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 apply this improved method in order to investigate the cluster-size dependence of the phase-separation tendency that has been proposed recently on the basis of calculations for smaller clusters. While the energy barrier associated with phase separation rapidly decreases with increasing cluster size for both hole and electron doping, the extension of the phase-separation region behaves differently in the two cases. More specifically, our results suggest that phase separation remains persistent in the hole-doped case and disappears in the electron-doped case. We also study the evolution of the single-particle spectrum as a function of doping and point out the relevance of our results for experimental findings in electron and hole-doped materials.