Regular Article - Theoretical Physics
Ergodic sampling of the topological charge using the density of states
Braid Technologies, Shibuya, 22412, Tokyo, Japan
2 School of Physics and Astronomy, The University of Edinburgh, EH9 3JZ, Edinburgh, UK
3 Centre for Mathematical Sciences, Plymouth University, PL4 8AA, Plymouth, UK
4 Department of Mathematics, Computational Foundry, Swansea University (Bay Campus), SA2 8EN, Swansea, UK
Accepted: 19 April 2021
Published online: 29 April 2021
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.
© The Author(s) 2021
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