Mass gap in the 2D O(3) nonlinear sigma model with aθ=πterm

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) nonlinear sigma model with a {theta} term in two 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.