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

TL;DR

This paper applies the tensor renormalization group to analyze the two-dimensional lattice CP(N-1) model, deriving a tensor network representation and confirming consistency with known models and simulations.

Contribution

The authors develop a tensor network representation for the CP(N-1) model with a $ heta$ term and demonstrate its consistency with existing models and Monte Carlo results.

Findings

Numerical results for CP(1) without $ heta$ match the O(3) model in the large $eta$ region.

Results are consistent with Monte Carlo simulations over a wide $eta$ range.

Tensor network approach is validated for the CP(N-1) model analysis.

Abstract

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 $\theta$ term is derived. We confirm that the numerical results of the CP(1) model without the $\theta$ term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\beta \gg 1$ and that obtained by the Monte Carlo simulation in a wider range of $\beta$. The numerical computation including the $\theta$ term is left for future challenges.