  Symmetry-protected topological $\left(SPT\right)$ phases are gapped
short-range entangled states with symmetry $G$, which can be systematically
described by group cohomology theory. $SU(3)$ and $SU(2)\times{U(1)}$ are
considered as the basic groups of Quantum Chromodynamics and
Weak-Electromagnetic unification, respectively. In two dimension $(2D)$,
nonlinear-sigma models with a quantized topological Theta term can be used to
describe nontrivial SPT phases. By coupling the system to a probe field and
integrating out the group variables, the Theta term becomes the effective
action of Chern-Simons theory which can derive the response current density. As
a result, the current shows a spin Hall effect, and the quantized number of the
spin Hall conductance of SPT phases $SU(3)$ and $SU(2)\times{U(1)}$ are same.
In addition, relationships between $SU(3)$ and $SU(2)\times{U(1)}$ which maps
$SU(3)$ to $SU(2)$ with a rotation $U(1)$ will be given.
