Phase structure of the CP(1) model in the presence of a topological $\theta$-term

• URL: http://arxiv.org/abs/2107.14220v2
• Date: Thu, 1 Sep 2022 14:02:20 GMT
• Title: Phase structure of the CP(1) model in the presence of a topological $\theta$-term
• Authors: Katsumasa Nakayama, Lena Funcke, Karl Jansen, Ying-Jer Kao, Stefan K\"uhn
• Abstract summary: We numerically study the phase structure of the CP(1) model in the presence of a topological $theta$-term. We compute the free energy for inverse couplings ranging from $0leq beta leq 1.1$ and find a CP-violating, first-order phase transition at $theta=pi$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We numerically study the phase structure of the CP(1) model in the presence of a topological $\theta$-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 $0\leq \beta \leq 1.1$ and find a CP-violating, first-order phase transition at $\theta=\pi$. In contrast to previous findings, our numerical results provide no evidence for a critical coupling $\beta_c<1.1$ above which a second-order phase transition emerges at $\theta=\pi$ and/or the first-order transition line bifurcates at $\theta\neq\pi$. If such a critical coupling exists, as suggested by Haldane's conjecture, our study indicates that is larger than $\beta_c>1.1$.

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