Lattice QCD noise reduction for bosonic correlators through blocking

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 space 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 density and squared field strength, finding noise reductions by ∼ 3 − 7 compared to the conventional approach on the same ensemble of configurations.

The sphaleron rate from 4D Euclidean lattices

“…One approach proposed recently [31,32] is to measure q(x) q(0) correlators as a function of Euclidean time and to attempt an analytic continuation to obtain the real-time spectral function, whose low-frequency limit determines Γ sphal,s . This is an interesting approach, but it is very challenging, particularly because of our ignorance of the expected low-frequency behavior of the spectral function and the challenge in reconstructing nontrivial low-frequency structures in such analytical continuations.…”