A meron cluster solution for the sign problem of the two-dimensional O(3) model

TL;DR

This paper introduces a meron cluster algorithm to address the sign problem in the two-dimensional O(3) model at theta=pi, enabling numerical simulations that reveal long-range correlations.

Contribution

It develops a novel cluster algorithm using meron clusters to effectively solve the sign problem in the 2D O(3) model at theta=pi.

Findings

Long-range correlations are observed at theta=pi.

The algorithm successfully generates configurations with only 0 and 2 merons.

The method improves the accuracy of correlation function estimations.

Abstract

The two-dimensional O(3) model at a vacuum angle theta=pi is investigated. This model has a severe sign problem. By a Wolff cluster algorithm an integer or half-integer topological charge is assigned to each cluster. The meron clusters (clusters with half-integer topological charge) are used to construct an improved estimator for the correlation function of two spins at theta=pi. Only configurations with 0 and 2 merons contribute to this correlation function. An algorithm, that generates configurations with only 0 and 2 merons, is constructed and numerical simulations at theta=pi are performed. The numerical results indicate the presence of long range correlations at theta=pi.