  The effect of the strong electron correlation on the topological phase
structure of 2-dimensional (2D) and 3D topological insulators is investigated,
in terms of lattice gauge theory. The effective model for noninteracting system
is constructed similarly to the lattice fermions with the Wilson term,
corresponding to the spin-orbit coupling. Introducing the electron-electron
interaction as the coupling to the gauge field, we analyze the behavior of
emergent orders by the strong coupling expansion methods. We show that there
appears a new phase with the in-plane antiferromagnetic order in the 2D
topological insulator, which is similar to the so-called "Aoki phase" in
lattice QCD with Wilson fermions. In the 3D case, on the other hand, there does
not appear such a new phase, and the electron correlation results in the shift
of the phase boundary between the topological phase and the normal phase.
