Multiscale Monte Carlo equilibration: Pure Yang-Mills theory

Abstract

We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.

29 pages, 19 figures; Eq. 7 - Eq. 9 modified (results unchanged); text added to Sec IV F; typos fixed; matches published version

References in corpus (5)

• Infinite N phase transitions in continuum Wilson loop operators
• Critical slowing down and error analysis in lattice QCD simulations
• Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
• Diffusion of topological charge in lattice QCD simulations
• Non-renormalizability of the HMC algorithm

Cited by in corpus (28)

• FLAG Review 2019
• FLAG Review 2021
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Axion phenomenology and $\theta$-dependence from $N_f=2+1$ lattice QCD
• Collins-Soper Kernel for TMD Evolution from Lattice QCD
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• FLAG Review 2024
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Machine learning action parameters in lattice quantum chromodynamics
• Lattice QCD and the anomalous magnetic moment of the muon
• Nonperturbative renormalization of staple-shaped Wilson line operators in lattice QCD
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
• Sparsening Algorithm for Multi-Hadron Lattice QCD Correlation Functions
• Proof of the renormalizability of the gradient flow
• Inverse Renormalization Group in Quantum Field Theory
• $Sp(2N)$ Yang-Mills theories on the lattice: scale setting and topology
• Quantum Yang-Mills theory: an overview of a programme
• Lattice QCD on Non-Orientable Manifolds
• Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations
• Scaling properties of multiscale equilibration
• Recent progress on QCD inputs for axion phenomenology
• Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors
• Generative learning for the problem of critical slowing down in lattice Gross Neveu model
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Sampling U(1) gauge theory using a re-trainable conditional flow-based model
• Multilevel Monte Carlo for quantum mechanics on a lattice
• Moments of pion distribution amplitude using operator product expansion on the lattice