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

We apply the higher-order tensor renormalization group to the lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $θ$ term is derived. We confirm that the numerical results of the CP(1) model without the $θ$ term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $β\gg 1$ and that obtained by the Monte Carlo simulation in a wider range of $β$. The numerical computation including the $θ$ term is left for future challenges.

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