Finite density 2d O(3) sigma model: dualization and numerical simulations

TL;DR

This paper reformulates the 2d O(3) sigma model to make its action real, enabling efficient Monte Carlo simulations to measure key physical observables like correlation functions and the mass gap.

Contribution

It introduces a dualization method that transforms the complex action into a real one, facilitating numerical simulations of the model.

Findings

Successful measurement of correlation functions

Determination of the mass gap

Validation of the dualization approach

Abstract

The action of the 2d O(3) non-linear sigma model on the lattice in a bath of particles, when expressed in terms of standard O(3) degrees of freedom, is complex. A reformulation of the model in terms of new variables that makes the action real is presented. This reshaping enables us to utilize Monte Carlo simulations based on usual importance sampling. Several observables, including the correlation function and the mass gap, are measured.