HMC and gradient flow with machine-learned classically perfect fixed-point actions

TL;DR

This paper uses machine learning to develop fixed-point lattice actions for SU(3) gauge theory, enabling more accurate continuum physics extraction with coarser lattices and proposing a classically perfect gradient flow.

Contribution

It introduces a machine-learned parameterization of fixed-point actions for SU(3) gauge theory and demonstrates their efficient simulation and potential for artifact-free gradient flow.

Findings

Superior parameterizations of fixed-point actions using neural networks.

Efficient Hybrid Monte Carlo simulation of these actions.

Initial results indicating scaling of the gradient flow.

Abstract

Fixed-point (FP) lattice actions are classically perfect, i.e., they have continuum classical properties unaffected by discretization effects and are expected to have suppressed lattice artifacts at weak coupling. Therefore they provide a possible way to extract continuum physics with coarser lattices, allowing to circumvent problems with critical slowing down and topological freezing towards the continuum limit. We use machine-learning methods to parameterize a FP action for four-dimensional SU(3) gauge theory using lattice gauge-covariant convolutional neural networks. The large operator space allows us to find superior parameterizations compared to previous studies and we show how such actions can be efficiently simulated with the Hybrid Monte Carlo algorithm. Furthermore, we argue that FP lattice actions can be used to define a classically perfect gradient flow without any lattice artifacts at tree level. We present initial results for scaling of the gradient flow with the FP action.