Alternatives to the stochastic "noise vector" approach

TL;DR

This paper investigates polynomial approximation methods as alternatives to noise vector techniques for estimating traces of inverse Dirac operators, which are crucial in QCD observables.

Contribution

It introduces polynomial approximation strategies as novel methods for trace estimation, offering potential improvements over traditional noise vector approaches.

Findings

Polynomial approximations can effectively estimate traces of inverse Dirac operators.

Alternative methods may reduce computational noise and improve accuracy.

The approach is applicable to key QCD observables like the quark condensate.

Abstract

Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers. Such traces are traditionally estimated with "noise vectors" sandwiching the operator. We explore alternative approaches based on polynomial approximations of the inverse Dirac operator.