Symmetries and exponential error reduction in Yang-Mills theories on the lattice

TL;DR

This paper introduces a multi-level Monte Carlo method leveraging symmetries in Yang-Mills theories to exponentially reduce computational costs when calculating correlation functions on the lattice.

Contribution

It proposes a novel multi-level Monte Carlo scheme exploiting symmetry properties to achieve exponential error reduction in lattice gauge theory computations.

Findings

Successful implementation in SU(3) Yang-Mills theory

Significant reduction in numerical effort for large time extents

Effective evaluation of parity odd state contributions

Abstract

The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the corresponding transfer matrix elements can be exploited to devise a multi-level Monte Carlo integration scheme for computing correlation functions whose numerical cost, at a fixed precision and at asymptotically large times, increases power-like with the time extent of the lattice. As a result the numerical effort is exponentially reduced with respect to the standard Monte Carlo procedure. We test this strategy in the SU(3) Yang--Mills theory by evaluating the relative contribution to the partition function of the parity odd states.