Phase structure analysis of CP(N-1) model using Tensor renormalization group

The phase structure of the lattice CP($N-1$) model in two dimensions is analyzed by the tensor renormalization group (TRG) method. We focus on the case $N=2$ and compare the numerical result of the TRG method with that of the strong-coupling analysis in the presence of the $\theta$ term and investigate the nature of the phase transition at $\theta =\pi$.