Phase diagram of the extended Hubbard model at weak coupling

The Hubbard model including nearest neighbor interaction is studied at T=0 on a d-dimensional hypercubic lattice (d much greater than 1) close to half filling. For the model in d=infinity we derive the exact result that the ground state at weak coupling is phase separated. Results for lower dimensions are then derived in a 1/d expansion. To obtain these results we first consider possible second order transitions. One then finds that the broken-symmetry phase near half filling is incommensurate. However, the corresponding ground state has negative compressibly and is hence thermodynamically unstable. A Maxwell construction is used to construct the actual phase separated ground state, which consists of homogeneous lower-density and antiferromagnetic or charge density wave higher-density regions. It is shown that both the doping level below which phase separation occurs and the order parameter differ from the corresponding Hartree results by a renormalization factor q of order unity. This renormalization factor q is calculated systematically up to O(1/D) in a 1/d expansion and turns out to be identical to the renormalization factor previously calculated for the low-temperature thermodynamics at half filling.