  The phase structure of the two dimensional lattice CP(1) model in the
presence of the $\theta$ term is analyzed by tensor network methods. The tensor
renormalization group, which is a standard renormalization method of tensor
networks, is used for the regions $\theta =0$ and $\theta \neq 0$. Loop-TNR,
which is more suitable for the analysis of near criticality, is also
implemented for the region $\theta =0$. The application of Loop-TNR for the
region $\theta \neq 0$ is left for future work.
