Algorithms for Disconnected Diagrams in Lattice QCD

TL;DR

This paper introduces an improved algorithm combining hierarchical probing and singular value deflation to efficiently compute disconnected diagrams in Lattice QCD, demonstrated through results on the chiral condensate and nucleon charges.

Contribution

It presents a novel algorithm that enhances the efficiency of calculating disconnected diagrams in Lattice QCD by leveraging hierarchical probing and singular value deflation.

Findings

Improved estimates of the chiral condensate.

More accurate nucleon charge calculations.

Reduced computational cost compared to basic methods.

Abstract

Computing disconnected diagrams in Lattice QCD (operator insertion in a quark loop) entails the computationally demanding problem of taking the trace of the all to all quark propagator. We first outline the basic algorithm used to compute a quark loop as well as improvements to this method. Then, we motivate and introduce an algorithm based on the synergy between hierarchical probing and singular value deflation. We present results for the chiral condensate using a 2+1-flavor clover ensemble and compare estimates of the nucleon charges with the basic algorithm.