Enhanced Sampling Techniques for Lattice Gauge Theory

TL;DR

This paper explores enhanced sampling methods like Metadynamics to overcome topological freezing in lattice gauge theories, improving simulation efficiency and autocorrelation times.

Contribution

It introduces strategies for accelerating bias potential buildup, volume extrapolation, and combines these with algorithmic improvements for better lattice gauge theory simulations.

Findings

Bias potentials reduce autocorrelation times significantly.

Volume extrapolation of potentials is feasible from small to large volumes.

Orthogonal algorithmic improvements further enhance sampling efficiency.

Abstract

In theories with topological sectors, such as lattice QCD and four-dimensional SU(N) gauge theories with periodic boundary conditions, conventional update algorithms suffer from topological freezing due to large action barriers separating distinct sectors. With appropriately constructed bias potentials, Metadynamics and related enhanced sampling techniques can mitigate this problem and significantly reduce the integrated autocorrelation times of the topological charge and associated observables. We test strategies to accelerate the buildup of bias potentials and the possibility of extrapolating potentials from small to large volumes. We also investigate the effectiveness of orthogonal algorithmic improvements, such as longer HMC trajectories and HMC variants, which may benefit conventional simulations as well.