  We construct a general wave function with the topological order by
introducing the $\mathbb{Z}_{2}$ gauge degrees of freedom, characterizing both
the toric code state and double semion state. Via calculating the correlation
length defined from the one-dimensional quantum transfer operator of the wave
function norm, we can map out the complete phase diagram in terms of the
parameter $\lambda $ and identify three different quantum critical points
(QCPs) at $\lambda =0$, $\pm 1.73$. The first one separates the toric code
phase and double semion phase, while later two describe the topological phase
transitions from the toric code phase or double semion phase to the symmetry
breaking phase, respectively. When mapping to the exactly solved statistical
models, the norm of the tensor network wave function is transformed into the
partition function of the eight-vertex model. Actually such a quantum-classical
mapping can not reveal the rich structures of low-energy excitations at these
three QCPs. So we further demonstrate that the full eigenvalue spectra of the
transfer operators with/without the flux insertions can describe the complete
quantum criticalities, which are characterized by the two-dimensional
compactified free boson conformal field theories (CFTs) with the compactified
radii $R=\sqrt{6}$ for the QCPs at $\lambda =\pm\sqrt{3}$ and $R=\sqrt{8/3}$
for the QCP at $\lambda =0$. For the QCP at $\lambda =0$, there are no anyon
condensation, and the emerged matrix product operator symmetries result in a
rich structure of the low-energy excitations, distinct from those of both toric
code and double semion phases. Finally, we discuss the possible relation
between our conformal quantum criticalities and the general (2+1) spatial-time
dimensional CFTs for quantum topological phase transitions.
