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2021

Riemannian manifold hybrid Monte Carlo in lattice QCD

Nguyen, Tuan, Boyle, Peter, Christ, Norman et al.

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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.

Riemannian manifold hybrid Monte Carlo in lattice QCD · Around

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S. Duane, R. Kenway, B.J. Pendleton and D. Roweth, Acceleration of gauge field dynamics , Physics Letters B 176
1986
Earlier work this paper cites.
A.D. Kennedy and B. Pendleton, Cost of the generalized hybrid Monte Carlo algorithm for free field theory , Nucl. Phys. B 607
2001
Earlier work this paper cites.
M. Girolami and B. Calderhead, Riemann manifold langevin and hamiltonian monte carlo methods , Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73
2010
Earlier work this paper cites.

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M. Lüscher, Properties and uses of the wilson flow in lattice qcd , Journal of High Energy Physics 2010
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M. Lüscher and S. Schaefer, Non-renormalizability of the HMC algorithm , Journal of High Energy Physics 2011
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Then

M. Lüscher and S. Schaefer, Lattice qcd without topology barriers , Journal of High Energy Physics 2011
2011
Later among the works it cites.
N.H. Christ and E.W. Wickenden, Fourier acceleration, the hmc algorithm and renormalizability , 2018
2018
Later among the works it cites.

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