Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions

TL;DR

This paper introduces a multigrid time slice blocking method for SU(2) lattice gauge theory, significantly reducing critical slowing down in two dimensions and exploring its extension to four dimensions with associated challenges.

Contribution

The paper develops and analyzes a multigrid algorithm for SU(2) lattice gauge theory, demonstrating its effectiveness in two dimensions and investigating its extension to four dimensions.

Findings

Critical slowing down is nearly eliminated in 2D.

The method's extension to 4D faces kinematical challenges due to local disorder.

Theoretical and numerical analysis supports the method's efficacy in 2D.

Abstract

We study a multigrid method for nonabelian lattice gauge theory, the time slice blocking, in two and four dimensions. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method. This result is in accordance with theoretical arguments based on the analysis of the scale dependence of acceptance rates for nonlocal Metropolis updates. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four dimensional gauge field leads to kinematical problems.