Locality and Efficient Evaluation of Lattice Composite Fields: Overlap-Based Gauge Operators

TL;DR

This paper introduces a new approach to the locality of lattice composite fields, demonstrating the local nature of overlap-based gauge operators in QCD and providing an efficient, volume-independent evaluation method for such non-ultralocal operators.

Contribution

It presents a novel framework for establishing locality in lattice composite fields and an efficient evaluation method for overlap-based operators with volume-independent computational cost.

Findings

Overlap-based gauge operators are shown to be local on realistic backgrounds.

The evaluation method's cost grows only logarithmically with decreasing accuracy.

The approach introduces the concept of exponential insensitivity to distant fields.

Abstract

We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix elements, showing for the first time their local nature on realistic path-integral backgrounds. The framework entails a method for efficient evaluation of such non-ultralocal operators, whose computational cost is volume-indepenent at fixed accuracy, and only grows logarithmically as this accuracy approaches zero. This makes computation of useful operators, such as overlap-based topological density, practical. The key notion underlying these features is that of exponential insensitivity to distant fields, made rigorous by introducing the procedure of statistical regularization. The scales associated with insensitivity property are useful characteristics of non-local continuum operators.