Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations

Abstract

We investigate the critical behaviour at theta=pi of the two-dimensional O(3) nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of theta, and on scaling transformations that allow a controlled analytic continuation to real values of theta. Our results are compatible with a second order phase transition, with the critical exponent of the SU(2)_1 Wess-Zumino-Novikov-Witten model, for sufficiently small values of the coupling.

Revised version. 24 pages, 7 figures

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• Topological Lattice Actions
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• Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case
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• First-principle simulations of 1+1d quantum field theories at $\theta =\pi$ and spin-chains
• Massive Schwinger model at finite $\theta$
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• 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
• Phase structure analysis of 2d lattice CP(1) model with $\theta$ term using tensor renormalization group method