Phase Separation in the Extended Hubbard Model at Weak Coupling

The Hubbard model including nearest-neighbor interaction is studied at $T=0\mathrm{}$ on a $d$-dimensional hypercubic lattice ($d\ge 3$) close to half filling. It is shown that the ground state at weak coupling is phase separated, consisting of homogeneous lower-density and antiferromagnetic or charge density wave higher-density regions. Incommensurate phases are unstable. The exact critical doping level and the exact order parameter are renormalized relative to the Hartree results. The renormalization factor at weak coupling turns out to be identical to the result found previously for the same model at half filling.