Ergodic sampling of the topological charge using the density of states

TL;DR

This paper introduces a density of states method with simulated tempering to improve ergodic sampling of topological charge in lattice gauge theories, significantly reducing autocorrelation times near the continuum limit.

Contribution

The authors develop a novel density of states approach combined with simulated tempering to enhance ergodicity and reduce autocorrelation in topological charge sampling in lattice gauge theory.

Findings

Significant reduction in autocorrelation times for topological charge.

Evidence of improved scaling properties near the continuum limit.

Enhanced ergodic sampling across topological sectors.

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.