  We consider an extended Hubbard model of interacting fermions on a lattice.
The fermion kinetic energy corresponds to a tight binding Hamiltonian with
nearest neighbour (-t) and next nearest neighbour (t') hopping matrix elements.
In addition to the onsite Hubbard interaction (U) we also consider a nearest
neighbour repulsion (V). We obtain the zero temperature phase diagram of our
model within the Hartree-Fock approximation. We consider ground states having
charge and spin density wave ordering as well as states with orbital
antiferromagnetism or spin nematic order. The latter two states correspond to
particle-hole binding with $d_{x^2-y^2}$ symmetry in the charge and spin
channels respectively. For $t' = 0$, only the charge density wave and spin
density wave states are energetically stable. For non-zero t', we find that
orbital antiferromagnetism (or spin nematic) order is stable over a finite
portion of the phase diagram at weak coupling. This region of stability is seen
to grow with increasing values of t'.
