  We present an exactly solvable spin-orbital model based on the Gamma-matrix
generalization of a Kitaev-type Hamiltonian. In the presence of small magnetic
fields, the model exhibits a critical phase with a spectrum characterized by
topologically protected Fermi points. Upon increasing the magnetic field, Fermi
points carrying opposite topological charges move toward each other and
annihilate at a critical field, signaling a phase transition into a gapped
phase with trivial topology in three dimensions. On the other hand, by
subjecting the system to a staggered magnetic field, an effective time-reversal
symmetry essential to the existence of three-dimensional topological insulators
is restored in the auxiliary free fermion problem. The nontrivial topology of
the gapped ground state is characterized by an integer winding number and
manifests itself through the appearance of gapless Majorana fermions confined
to the two-dimensional surface of a finite system.
