  The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb
lattice and, at strong coupling, interpolates between the Heisenberg model and
the Kitaev model. It is basically a Hubbard model with ordinary hopping $t$ and
spin-dependent hopping $t'$. We study this model in the weak to intermediate
coupling regime, at half-filling, using the Cellular Dynamical Impurity
Approximation (CDIA), an approach related to Dynamical Mean Field Theory but
based on Potthoff's variational principle. We identify four phases in the
$(U,t')$ plane: two semi-metallic phases with different numbers of Dirac
points, an antiferromagnetic insulator, and an algebraic spin liquid. The last
two are separated by a first-order transition. These four phases all meet at a
single point and could be realized in cold atom systems.
