Riemannian manifold hybrid Monte Carlo in lattice QCD

TL;DR

This paper introduces a Riemannian Manifold HMC algorithm variant for lattice QCD that uses spectral information of the gauge covariant Laplacian to mitigate critical slowing down at small lattice spacings.

Contribution

It develops spectral tools with Chebyshev filters to optimize and monitor the RMHMC algorithm's acceleration in lattice QCD simulations.

Findings

Spectral analysis enables optimization of the RMHMC mass term.

Tools provide insights into force spectra for better algorithm tuning.

Potential to reduce critical slowing down in lattice QCD calculations.

Abstract

Critical slowing down presents a critical obstacle to lattice QCD calculation at the smaller lattice spacings made possible by Exascale computers. Inspired by the concept of Fourier acceleration, we study a version of the Riemannian Manifold HMC (RMHMC) algorithm in which the canonical mass term of the HMC algorithm is replaced by a rational function of the SU(3) gauge covariant Laplacian. We have developed a suite of tools using Chebyshev filters based on the SU(3) gauge covariant Laplacian that provides the power spectra of both the gauge and fermion forces and determines the spectral dependence of the resulting RMHMC evolution of long- and short-distance QCD observables. These tools can be used to optimize the RMHMC mass term and to monitor the resulting acceleration mode-wise.