Equivariant flow-based sampling for lattice gauge theory

TL;DR

This paper introduces a gauge-invariant flow-based sampling method for lattice gauge theories, demonstrating significant efficiency improvements over traditional methods near critical points in U(1) gauge theory.

Contribution

It presents a novel machine learning framework for gauge-invariant sampling in lattice gauge theories, specifically applied to U(1) in two dimensions.

Findings

Order of magnitude more efficient sampling near critical points

Effective at sampling topological quantities

Outperforms Hybrid Monte Carlo and Heat Bath methods

Abstract

We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that near critical points in parameter space the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as Hybrid Monte Carlo and Heat Bath.