  We study the strong coupling limit of the extended Hubbard model in two
dimensions. The model consists of hopping, on-site interaction,
nearest-neighbor interaction, spin-orbit coupling and Zeeman spin splitting.
While the study of this model is motivated by a search for topological phases
and in particular a topological superconductor, the methodology we develop may
be useful for a variety of systems. We begin our treatment with a canonical
transformation of the Hamiltonian to an effective model which is appropriate
when the (quartic) interaction terms are larger than the (quadratic) kinetic
and spin-orbit coupling terms. We proceed by analyzing the strong coupling
model variationally. Since we are mostly interested in a superconducting phase
we use a Gutzwiller projected BCS wavefunction as our variational state. To
continue analytically we employ the Gutzwiller approximation and compare the
calculated energy with Monte-Carlo calculations. Finally we determine the
topology of the ground state and map out the topology phase diagram.
