Flow-based sampling for fermionic lattice field theories

TL;DR

This paper develops flow-based sampling methods for fermionic lattice field theories, enabling more accurate and efficient simulations of complex quantum systems involving fermions, with practical applications demonstrated on a 2D Yukawa-coupled fermion-scalar model.

Contribution

It introduces novel flow-based algorithms tailored for fermionic theories, extending previous scalar and gauge theory approaches to include dynamical fermions.

Findings

Successfully sampled configurations of a 2D massless fermion-scalar system.

Demonstrated the effectiveness of flow-based methods for fermionic lattice theories.

Provided a foundation for applying these techniques to Standard Model and condensed matter systems.

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.