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International Symposium on Lattice Field Theory (LATTICE)

Phase structure analysis of 2d CP(1) model with $\theta$ term by tensor renormalization group

Hayato Aizawa, Shinji Takeda, Yusuke Yoshimura

Published Feb 10, 2025• 0 citations
Publisher

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.

DOI
10.22323/1.466.0371

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Phase structure analysis of CP(1) model with θθθ term by tensor renormalization group
We analyze the phase structure of 2d lattice CP(1) model with θθθ 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 θ=πθ=πθ=π, which is consistent with the Haldane's conjecture.
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Phase structure of the CP(1) model in the presence of a topological θ\thetaθ-term
We numerically study the phase structure of the CP(1) model in the presence of a topological θ\thetaθ-term, a regime afflicted by the sign problem for conventional lattice Monte Carlo simulations. Using a bond-weighted Tensor Renormalization Group method, we compute the free energy for inverse couplings ranging from 0≤β≤1.10\leq \beta \leq 1.10≤β≤1.1 and find a CP-violating, first-order phase transition at θ=π\theta=\piθ=π. In contrast to previous findings, our numerical results provide no evidence for a critical coupling βc<1.1\beta_c<1.1βc​<1.1 above which a second-order phase transition emerges at θ=π\theta=\piθ=π and/or the first-order transition line bifurcates at θ≠π\theta\neq\piθ=π. If such a critical coupling exists, as suggested by Haldane's conjecture, our study indicates that is larger than βc>1.1\beta_c>1.1βc​>1.1.