Control variates for lattice field theory

TL;DR

This paper introduces a method using control variates derived from lattice Schwinger-Dyson relations to improve the signal-to-noise ratio in lattice field theory simulations, demonstrated on 2D scalar models.

Contribution

The paper presents a systematic approach to construct control variates for lattice field theories, addressing the exponential signal-to-noise problem.

Findings

Improved signal-to-noise ratio in 2D scalar lattice models

Control variates effectively reduce statistical noise

Strategy outlined for scaling to larger lattice systems

Abstract

In most lattice field theories, correlators are plagued by a signal-to-noise problem of exponential difficulty in the time separation. We propose a method for improving the signal-to-noise ratio, in which control variates are systematically constructed from lattice Schwinger-Dyson relations. The method is demonstrated on various two-dimensional lattices in scalar field theory, and a strategy for scaling to larger systems is explored.