I just found that I made a foolish misunderstanding of prof.Wen's paper. In fact, the operator $\psi_i=(\psi_{1i},\psi_{2i})^T=(f_{1i},f_{2i}^\dagger)^T$ and $\mathbf{S_i}=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$, but I misunderstood $\mathbf{S_i}=\frac{1}{2}\psi_i^\dagger\mathbf{\sigma}\psi_i$ before(Please see Eq.(8) in this paper http://prb.aps.org/abstract/PRB/v65/i16/e165113 at the very beginning).

Now everything goes well. In fact, the $SU(2)$ gauge transformations $\psi_i \rightarrow G_i\psi_i$ are totally equivalent to $\bigl(\begin{smallmatrix} f_{1i} & -f_{2i}^\dagger\\ f_{2i} & f_{1i}^\dagger \end{smallmatrix}\bigr)\rightarrow \bigl(\begin{smallmatrix} f_{1i} & -f_{2i}^\dagger\\ f_{2i} & f_{1i}^\dagger \end{smallmatrix}\bigr)G_i$. And the $SU(2)$ matrices being on the left or right depends on the notation of spinon operartors that you define, which is not the key point here.

God, I just found that I made a very foolish misunderstanding of prof.Wen's paper. In fact, the operator $\psi_i=(\psi_{1i},\psi_{2i})^T=(f_{1i},f_{2i}^\dagger)^T$ and $\mathbf{S_i}=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$, but I misunderstood $\mathbf{S_i}=\frac{1}{2}\psi_i^\dagger\mathbf{\sigma}\psi_i$ before(Please see Eq.(8) in this paper http://prb.aps.org/abstract/PRB/v65/i16/e165113 at the very beginning).

Now everything goes well. In fact, the $SU(2)$ gauge transformations $\psi_i \rightarrow G_i\psi_i$ are totally equivalent to $\bigl(\begin{smallmatrix} f_{1i} & -f_{2i}^\dagger\\ f_{2i} & f_{1i}^\dagger \end{smallmatrix}\bigr)\rightarrow \bigl(\begin{smallmatrix} f_{1i} & -f_{2i}^\dagger\\ f_{2i} & f_{1i}^\dagger \end{smallmatrix}\bigr)G_i$. And the $SU(2)$ matrices being on the left or right depends on the notation of spinon operartors that you define, which is not the key point here.

Note: The operators $\psi_i$ that appear in all of Wen's papers on PSG in 2002 are not the direct annihilation operators for Schwinger-fermions $f_i$, so please be very careful!