Learning the generating functional for variance reduction in lattice QCD
Authors: Ryan Abbott, Yang Fu, Daniel C. Hackett, Gurtej Kanwar, Fernando Romero-López, Phiala E. Shanahan
Organizations: 1Physics Department, Columbia University, New York, NY 10027, USA · Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · 3The NSF AI Institute for Artificial Intelligence and Fundamental Interactions · 4Fermi National Accelerator Laboratory, Batavia, IL 60510, U.S.A. · 5Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, EH9 3FD Edinburgh, United Kingdom · 6Albert Einstein Center, Institute for Theoretical Physics, University of Bern, 3012 Bern, Switzerland
The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary N-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.