  The dimerized Kane-Mele model with/without the strong interaction is studied
using analytical methods. The boundary of the topological phase transition of
the model without strong interaction is obtained. Our results show that the
occurrence of the transition only depends on dimerized parameter . From the
one-particle spectrum, we obtain the completed phase diagram including the
quantum spin Hall (QSH) state and the topologically trivial insulator. Then,
using different mean-field methods, we investigate the Mott transition and the
magnetic transition of the strongly correlated dimerized Kane-Mele model. In
the region between the two transitions, the topological Mott insulator (TMI)
with characters of Mott insulators and topological phases may be the most
interesting phase. In this work, effects of the hopping anisotropy and Hubbard
interaction U on boundaries of the two transitions are observed in detail. The
completed phase diagram of the dimerized Kane-Mele-Hubbard model is also
obtained in this work. Quantum fluctuations have extremely important influences
on a quantum system. However, investigations are under the framework of the
mean field treatment in this work and the effects of fluctuations in this model
will be discussed in the future.
