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

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arxiv 2107.14220 v2 pith:DJSYHLPD submitted 2021-07-29 hep-lat cond-mat.str-elquant-ph

Katsumasa Nakayama , Lena Funcke , Karl Jansen , Ying-Jer Kao , Stefan Kühn This is my paper · ORCID
classification hep-latcond-mat.str-elquant-ph
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method

    hep-lat 2026-02 conditional novelty 7.0 of 10

    Forward-mode AD for TRG is derived with (k+1)(k+2)/2 cost scaling, linked to impurity methods, and tested on the 2D/3D Ising model for energy, specific heat, and critical exponents.

  2. Tensor renormalization group study of cold and dense QCD in the strong coupling limit

    hep-lat 2026-01 conditional novelty 6.0 of 10

    In strong-coupling lattice QCD at Nτ=8, the chiral and nuclear transition endpoints coincide at m_c≈2.06, and a first-order transition persists at m=2.07 on a 1024^4 zero-temperature lattice.

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

    hep-lat 2025-02 conditional novelty 6.0 of 10

    Numerical tensor-network results locate a critical point at theta=pi in the 2D CP(1) model, consistent with Haldane's conjecture.

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