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

TL;DR

This paper investigates the mass gap behavior in the 2D O(3) non-linear sigma model with a theta term, using analytic continuation from imaginary theta data, and introduces a new simulation algorithm to study topological effects.

Contribution

It introduces a modified cluster algorithm for simulating the model with imaginary theta and demonstrates the massless point at theta≈3.10, providing new insights into the Haldane conjecture.

Findings

Massless point at theta≈3.10(5).

Successful simulation with a new cluster algorithm.

Validation of analytic continuation methods.

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.