Lattice QCD noise reduction for bosonic correlators through blocking

TL;DR

This paper introduces a blocking method to significantly enhance the signal-to-noise ratio in lattice QCD bosonic correlators, especially for disconnected contributions, by binning and fitting short-distance correlations.

Contribution

The proposed blocking technique improves noise reduction in lattice correlators by capturing short-distance correlations exactly and fitting large-distance parts, with minimal additional computational cost.

Findings

Achieved noise reductions by a factor of 3-7 in topological charge density correlators.

Applicable to zero momentum correlators with larger in-plane dimensions than separation.

Method effectively enhances signal quality with marginal computational overhead.

Abstract

We propose a method to substantially improve the signal-to-noise ratio of lattice correlation functions for bosonic operators or other operator combinations with disconnected contributions. The technique is applicable for correlations between operators on two planes (zero momentum correlators) when the dimension of the plane is larger than the separation between the two planes which are correlated. In this case, the correlation arises primarily from points whose in-plane coordinates are close, but noise arises from all pairs of points. By breaking each plane into bins and computing bin-bin correlations, it is possible to capture these short-distance correlators exactly while replacing (small) correlators at large spatial extent with a fit, with smaller uncertainty than the data. The cost is only marginally larger than averaging each plane before correlating, but the improvement in signal-to-noise can be substantial. We test the method on correlators of the gradient-flowed topological charge density and squared field strength, finding noise reductions by a factor of $\sim$ 3$-$7 compared to the conventional approach on the same ensemble of configurations.