Exploring efficient methods for precision QCD calculations on the lattice

Abstract

We study a new technique for stochastic noise reduction in the calculation of propagators by implementing it in OpenQ*D for two ensembles with O(a) improved Wilson fermion ac- tion, with periodic boundary conditions and pion masses of 437MeV and 331MeV, for the connected and disconnected vector and pseudoscalar correlators. The technique performs low-mode averaging using the low-lying spectrum of the spatial Laplacian operator instead of the Dirac operator. We find that the technique yields no speedup compared to traditional methods, owing to the failure of its underlying assumption that the spectra of the spatial Laplacian and Dirac operators are sufficiently similar for the technique’s purposes. However, the overlap is also found to be sensitive to rescaling the Laplacian by a real number, significantly enhancing performance. While still falling short of cost-effectiveness, we conclude that this suggests that the overlap of the low-lying operator spectrum with physical observables is sensitive to small changes, and future modifications may yet yield a cheaper alternative to the Dirac operator for low-mode averaging. We further tested the ability of generative flow-based models based on neural networks to sample from the Lüscher action of the 2D U(1) Schwinger model. The Lüscher action approximates the fermion determinant through a polynomial, resulting in a local action of nl additional multi-boson fields. Flow-based models we trained for < 20, 000 update steps on a single Google Colab GPU proved able to sample from the Lüscher action for the Schwinger model on a L/a = 8 lattice with nL = 12 multi-boson fields, and on a L/a = 16 lattice with nL = 4 multi-boson fields. The models use the same fermionic layers for all the multi-boson fields. Thus, their total parameter count is not extensive in nL. We conclude that with further algorithmic improvement, domain decomposition using the Lüscher action seems to be a promising avenue for enabling the sampling of significantly larger lattice volumes with flow-based models.