The $\theta$-term, CP${}^{N-1}$ Model and the Inversion Approach in the Imaginary $\theta$ Method

Abstract

The weak coupling region of CP${}^{N-1}$ lattice field theory with the $\theta$-term is investigated. Both the usual real theta method and the imaginary theta method are studied. The latter was first proposed by Bhanot and David. Azcoiti et al. proposed an inversion approach based on the imaginary theta method. The role of the inversion approach is investigated in this paper. A wide range of values of $h=-\mathrm{Im}\theta$ is studied, where $\theta$ denotes the magnitude of the topological term. Step-like behavior in the $x$-$h$ relation (where $x=Q/V$, $Q$ is the topological charge, and $V$ is the two dimensional volume) is found in the weak coupling region. The physical meaning of the position of the step-like behavior is discussed. The inversion approach is applied to weak coupling regions.

PTPTEX<ver.0.9>, 17 pages with 13 figures. Some sentences were corrected

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• New proposal for numerical simulations of theta-vacuum like systems
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• Monte Carlo Studies of Two-Dimensional Systems with a $\theta$ Term
• Two dimensional CP^2 Model with θ-term and Topological Charge Distributions
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Cited by in corpus (6)

• Generalization of the Haldane conjecture to SU(3) chains
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Fractionally charged Wilson loops as a probe of $\theta$-dependence in $C{P}^{N-1}$ sigma models: Instantons vs. large N
• Self-conjugate representation SU(3) chains
• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations