Numerical study of the mass spectrum in the 2D O(3) sigma model with a theta term

TL;DR

This study uses a modified cluster algorithm to numerically investigate the mass spectrum of the 2D O(3) sigma model with a theta term, inferring properties at real theta from simulations at imaginary theta.

Contribution

Introduces a modified Swendsen-Wang cluster algorithm to simulate the model with a theta term and uses analytic continuation to study the mass spectrum.

Findings

Evidence of an excited state in the mass spectrum at certain theta values

Method enables investigation of models with sign problems

Provides insights into the decay of states as theta varies

Abstract

It has been conjectured that the mass spectrum of the O(3) non-linear sigma model with a theta term in 2 dimensions may possess an excited state, which decays when theta is lowered from pi below a critical value. Since the direct numerical investigation of the model is prevented by a sign problem, we try to infer some information on the mass spectrum at real theta by studying the model at imaginary theta via analytic continuation. A modified Swendsen-Wang cluster algorithm has been introduced to simulate the model with the theta term.