Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling

Abstract

At fine lattice spacings, Markov chain Monte Carlo simulations of QCD and other gauge theories with or without fermions are plagued by slow modes that give rise to large autocorrelation times. This can lead to simulation runs that are effectively stuck in one topological sector, a problem known as topological freezing. Here, we demonstrate that for a relevant set of parameters, Metadynamics can be used to unfreeze 4-dimensional SU(3) gauge theory. However, compared to local update algorithms and the Hybrid Monte Carlo algorithm, the computational overhead is significant in pure gauge theory, and the required reweighting procedure may considerably reduce the effective sample size. To deal with the latter problem, we propose modifications to the Metadynamics bias potential and the combination of Metadynamics with parallel tempering. We test the new algorithm in 4-dimensional SU(3) gauge theory and find that it can achieve topological unfreezing without compromising the effective sample size, thereby reducing the autocorrelation times of topological observables by at least two orders of magnitude compared to conventional update algorithms. Additionally, we observe significantly improved scaling of autocorrelation times with the lattice spacing in 2-dimensional U(1) gauge theory.

23 pages, 12 figures, 8 tables. v2: Matches published version

References in corpus (59)

• Escaping free-energy minima
• Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• Properties and uses of the Wilson flow in lattice QCD
• Analytic Smearing of SU(3) Link Variables in Lattice QCD
• FLAG Review 2021
• Equilibrium free energies from non-equilibrium metadynamics
• The Nf=0 heavy quark potential from short to intermediate distances
• High-precision scale setting in lattice QCD
• Trivializing maps, the Wilson flow and the HMC algorithm
• Monte Carlo errors with less errors
• Critical slowing down and error analysis in lattice QCD simulations
• Lattice QCD without topology barriers
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Equivariant flow-based sampling for lattice gauge theory
• Lattice QCD at the physical point: Simulation and analysis details
• Theta dependence of SU(N) gauge theories
• Finite volume QCD at fixed topological charge
• QCD at Fixed Topology
• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
• Sampling using $SU(N)$ gauge equivariant flows
• Critical slowing down of topological modes
• Hybrid Monte Carlo and topological modes of full QCD
• Rationale for UV-filtered clover fermions
• Precision study of the SU(3) topological susceptibility in the continuum
• Improving the Chiral Properties of Lattice Fermions
• Topology in full QCD at high temperature: a multicanonical approach
• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Universality and scaling behavior of RG gauge actions
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Stochastic locality and master-field simulations of very large lattices
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• The Kaon B-parameter from Quenched Domain-Wall QCD
• Flow-based sampling in the lattice Schwinger model at criticality
• Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
• Learning Lattice Quantum Field Theories with Equivariant Continuous Flows
• Metadynamics Surfing on Topology Barriers: the $C{P}^{N-1}$ Case
• Learning Trivializing Gradient Flows for Lattice Gauge Theories
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Physics of eta-prime with rooted staggered quarks
• Measure of Autocorrelation Times of Local Hybrid Monte Carlo Algorithm for Lattice QCD
• Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants
• Testing trivializing maps in the Hybrid Monte Carlo algorithm
• Topological Zero Modes in Monte Carlo Simulations
• Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse
• Three topics in the Schwinger model
• Ergodic sampling of the topological charge using the density of states
• Parallel Tempering in Lattice QCD with O(a)-Improved Wilson Fermions
• Flow-based density of states for complex actions
• Lattice QCD on Non-Orientable Manifolds
• Scaling properties of multiscale equilibration
• Parallel tempering in full QCD with Wilson fermions
• Testing algorithms for critical slowing down
• Multiscale Monte Carlo equilibration: Two-color QCD with two fermion flavors
• The topological properties of QCD at high temperature: problems and perspectives
• Topology on the lattice; 2d Yang-Mills theories with a theta term
• Topology changing update algorithms for SU(3) gauge theory
• Calculation of weak matrix elements in domain-wall QCD with the DBW2 gauge action

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