Phase structure analysis of CP(1) model with $\theta$ term by tensor renormalization group

TL;DR

This paper investigates the phase structure of the 2D lattice CP(1) model with a $ heta$ term using tensor renormalization group methods, revealing a critical point at $ heta=\pi$ consistent with Haldane's conjecture.

Contribution

It introduces a new tensor network representation for the CP(1) model with improved accuracy and applies tensor renormalization group to analyze its phase structure.

Findings

Critical point at $ heta=\pi$ identified

Tensor network representation with quadrature scheme proposed

Results support Haldane's conjecture

Abstract

We analyze the phase structure of 2d lattice CP(1) model with $\theta$ term by using the bond-weighted tensor renormalization group method. We propose a new tensor network representation for the model using the quadrature scheme and confirm that its accuracy is better than that of the conventional character-like expansion. As a probe to study the phase structure, we adopt the central charge and the scaling dimensions. The numerical results indicate an existence of critical point at $\theta=\pi$, which is consistent with the Haldane's conjecture.