Loop-TNR analysis of CP(1) model with theta term

TL;DR

This paper applies tensor network methods, including tensor renormalization group and Loop-TNR, to analyze the phase structure of the 2D lattice CP(1) model with a theta term, focusing on different theta regions.

Contribution

It introduces the use of Loop-TNR for the CP(1) model at theta=0, providing a more suitable analysis near criticality, and compares it with standard tensor renormalization group methods.

Findings

Loop-TNR effectively analyzes the CP(1) model at theta=0 near criticality.

Tensor renormalization group is used for theta ≠ 0 regions.

Future work planned for applying Loop-TNR to theta ≠ 0 regions.

Abstract

The phase structure of the two dimensional lattice CP(1) model in the presence of the $\theta$ term is analyzed by tensor network methods. The tensor renormalization group, which is a standard renormalization method of tensor networks, is used for the regions $\theta =0$ and $\theta \neq 0$. Loop-TNR, which is more suitable for the analysis of near criticality, is also implemented for the region $\theta =0$. The application of Loop-TNR for the region $\theta \neq 0$ is left for future work.