Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term

Abstract

By analytic continuation to real theta of data obtained from numerical simulation at imaginary theta we study the Haldane conjecture and show that the O(3) non-linear sigma model with a theta term in 2 dimensions becomes massless at theta=3.10(5). A modified cluster algorithm has been introduced to simulate the model with imaginary theta. Two different definitions of the topological charge on the lattice have been used; one of them needs renormalization to match the continuum operator. Our work also offers a successful test for numerical methods based on analytic continuation.

Latex file, 4 pages. To appear in PRD; it contains the justification of analicity, more details about the fits, more references, etc

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• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
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• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations
• Renormalization of the Nonlinear O(3) Model with Theta-Term
• Phase structure analysis of 2d lattice CP(1) model with $\theta$ term using tensor renormalization group method
• The interplay of the sign problem and the infinite volume limit: gauge theories with a theta term
• Numerical study of the mass spectrum in the 2D O(3) sigma model with a theta term