  Landau's symmetry breaking theory is the basis of modern condensed matter
physics, from which most phases can be understood. The recent discovery of
topological insulators simulates the study on the topological phase which is
beyond this theory. An interesting question is whether the topological phase
and spontaneous symmetry breaking order can coexist. We study this problem
based on the topological phase in the Haldane model. Firstly by including a
staggered potential, we show that if the system is subjected to the symmetry
needed by the charge density wave (CDW) order in advance, the topological phase
can coexist with the CDW order, realizing the topological CDW phase. While when
the nearest neighor interaction which preserves the symmetry of the origin
Hamiltonian is included, the CDW order can not develop from spontaneous
symmetry breaking in the topological phase. The results imply that a
spontaneous symmetry breaking order may not develop in a topological phase.
