Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model

Abstract

The validity of the Haldane's conjecture entails that the mass gap of the 2-dimensional O(3) non-linear sigma model with a $\theta$-term must tend to zero as $\theta$ approaches the value $\pi$ by following a precise law. In the present paper we extract the related critical exponents by simulating the model at imaginary $\theta$.

arXiv comment24 pages, LaTeX source and 5 eps figures

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Cited by in corpus (18)

• Generalization of the Haldane conjecture to SU(3) chains
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• $\theta$ dependence in $SU(3)$ Yang-Mills theory from analytic continuation
• Tensor renormalization group analysis of CP(N-1) model
• Topological critical slowing down: variations on a toy model
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Flag manifold sigma models: spin chains and integrable theories
• Peeking into the $\theta$ vacuum
• Is $N=2$ Large?
• Self-conjugate representation SU(3) chains
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta =\pi$ term
• Loop-TNR analysis of CP(1) model with theta term
• Strong CP problem in the quantum rotor
• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations
• The interplay of the sign problem and the infinite volume limit: gauge theories with a theta term