Locality and Statistical Error Reduction on Correlation Functions

TL;DR

This paper introduces a multilevel Monte-Carlo method that reduces statistical errors in correlation function measurements for local actions, with efficiency gains depending on the low-energy spectrum.

Contribution

The paper presents a novel multilevel Monte-Carlo scheme tailored for local actions, demonstrating its effectiveness in reducing errors in correlation functions.

Findings

Efficiency increases exponentially with time separation for Wilson loop correlations.

The method's performance depends on the low-energy spectrum of the system.

Application to SU(3) gauge theory shows significant error reduction.

Abstract

We propose a multilevel Monte-Carlo scheme, applicable to local actions, which is expected to reduce statistical errors on correlation functions. We give general arguments to show how the efficiency and parameters of the algorithm are determined by the low-energy spectrum. As an application, we measure the euclidean-time correlation of pairs of Wilson loops in SU(3) pure gauge theory with constant relative errors. In this case the ratio of the new method's efficiency to the standard one increases as exp{m_0t/2}, where m_0 is the mass gap and t the time separation.