We analyze the phase structure of 2d lattice CP(1) model with $\theta$ term by using the bond-weighted tensor renormalization group method.
We propose a new tensor network representation for the model using the quadrature scheme and confirm that its accuracy is better than that of the conventional character-like expansion.
As a probe to study the phase structure, we adopt the central charge and the scaling dimensions.
The numerical results indicate an existence of critical point at $\theta=\pi$, which is consistent with the Haldane's conjecture.