Hybrid Monte Carlo Simulation with Fourier Acceleration of the $N=2$ Principal Chiral Model in two Dimensions

TL;DR

This paper demonstrates that Fourier-accelerated Hybrid Monte Carlo significantly improves simulation efficiency for the two-dimensional SU(2) principal chiral model, enabling high-precision results and verification of asymptotic scaling.

Contribution

The study introduces Fourier Acceleration into Hybrid Monte Carlo for the 2D SU(2) model, greatly reducing critical slowing down and enhancing simulation speed and accuracy.

Findings

Simulation efficiency increased by up to 300 times.

Achieved high-precision numerical predictions.

Verified the onset of asymptotic scaling.

Abstract

Motivated by the similarity to QCD, specifically the property of asymptotic freedom, we simulate the dynamics of the SU(2) $\times$ SU(2) model in two dimensions using the Hybrid Monte Carlo algorithm. By introducing Fourier Acceleration, we show that critical slowing down is largely avoided and increases the simulation efficiency by up to a factor of 300. This yields numerical predictions at a precision exceeding that of existing studies and allows us to verify the onset of asymptotic scaling.