Ergodic sampling of the topological charge using the density of states

Abstract

In lattice calculations, the approach to the continuum limit is hindered by the severe freezing of the topological charge, which prevents ergodic sampling in configuration space. In order to significantly reduce the autocorrelation time of the topological charge, we develop a density of states approach with a smooth constraint and use it to study SU(3) pure Yang Mills gauge theory near the continuum limit. Our algorithm relies on simulated tempering across a range of couplings, which guarantees the decorrelation of the topological charge and ergodic sampling of topological sectors. Particular emphasis is placed on testing the accuracy, efficiency and scaling properties of the method. In their most conservative interpretation, our results provide firm evidence of a sizeable reduction of the exponent z related to the growth of the autocorrelation time as a function of the inverse lattice spacing.

22 pages, 16 figure

References in corpus (7)

• Critical slowing down and error analysis in lattice QCD simulations
• Finite volume QCD at fixed topological charge
• The density of states in gauge theories
• The density of states approach to dense quantum systems
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• New DoS approaches to finite density lattice QCD

Cited by in corpus (9)

• SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing
• Topological sampling through windings
• Color dependence of the topological susceptibility in Yang-Mills theories
• $Sp(2N)$ Yang-Mills theories on the lattice: scale setting and topology
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Efficient computations of continuous action densities of states for lattice models