Locality and exponential error reduction in numerical lattice gauge theory

TL;DR

This paper introduces a multilevel numerical scheme leveraging locality in non-abelian gauge theories to exponentially reduce errors in calculating large Wilson loops, significantly improving simulation efficiency.

Contribution

The authors develop and demonstrate a multilevel approach that exploits locality to achieve exponential error reduction in lattice gauge theory computations.

Findings

Error reduction is exponential with the multilevel scheme.

Efficiency improves by orders of magnitude for large loops.

Effective for SU(3) Polyakov loop correlation functions.

Abstract

In non-abelian gauge theories without matter fields, expectation values of large Wilson loops and loop correlation functions are difficult to compute through numerical simulation, because the signal-to-noise ratio is very rapidly decaying for increasing loop sizes. Using a multilevel scheme that exploits the locality of the theory, we show that the statistical errors in such calculations can be exponentially reduced. We explicitly demonstrate this in the SU(3) theory, for the case of the Polyakov loop correlation function, where the efficiency of the simulation is improved by many orders of magnitude when the area bounded by the loops exceeds 1 fm^2.