Abstract
Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory, proof-of-principle studies have demonstrated the effectiveness of this approach for scalar theories, gauge theories, and statistical systems. This work develops approaches that enable flow-based sampling of theories with dynamical fermions, which is necessary for the technique to be applied to lattice field theory studies of the Standard Model of particle physics and many condensed matter systems. As a practical demonstration, these methods are applied to the sampling of field configurations for a two-dimensional theory of massless staggered fermions coupled to a scalar field via a Yukawa interaction.
Highlights
Lattice field theory is among the most successful approaches for regularizing and computing path integral expectation values in quantum field theory
This work develops approaches that enable flow-based sampling of theories with dynamical fermions, which is necessary for the technique to be applied to lattice field theory studies of the Standard Model of particle physics and many condensed matter systems
The path integral can be numerically evaluated by formulating a stochastic process weighted by the Euclidean lattice action and applying Markov Chain Monte Carlo (MCMC) sampling [1]
Summary
Lattice field theory is among the most successful approaches for regularizing and computing path integral expectation values in quantum field theory. Specialized Markov chain steps have been developed in a number of specific contexts, including cluster updates [14,15,16,17,18,19,20,21,22], worm algorithms [23,24,25], sampling in terms of dual variables [26,27,28], and event-chain algorithms [29,30,31,32,33] Though these methods have been shown to mitigate critical slowing down in some settings, they cannot be applied to many theories of interest, including lattice QCD.
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