Tensor renormalization group analysis of ${\rm CP}(N-1)$ model in two dimensions

We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of CP($N-1$) model 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 Monte Carlo simulation in a wider range of $β$.

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