  The dual-fermion approach offers a way to perform diagrammatic expansion
around the dynamical mean-field theory. Using this formalism, the influence of
antiferromagnetic fluctuations on the self-energy is taken into account through
ladder-type diagrams in the particle-hole channel. The resulting phase diagram
for the (quasi-)two-dimensional Hubbard model exhibits antiferromagnetism and
d-wave superconductivity. Furthermore, a uniform charge instability, i.e.,
phase separation, is obtained in the low doping regime around the Mott
insulator. We also examine spin/charge density wave fluctuations including
d-wave symmetry. The model exhibits a tendency towards an unconventional charge
density-wave, but no divergence of the susceptibility is found.
