Diffusion of topological charge in lattice QCD simulations

Abstract

We study the autocorrelations of observables constructed from the topological charge density, such as the topological charge on a time slice or in a subvolume, using a series of hybrid Monte Carlo simulations of pure SU(3) gauge theory with both periodic and open boundary conditions. We show that the autocorrelation functions of these observables obey a simple diffusion equation and we measure the diffusion coefficient, finding that it scales like the square of the lattice spacing. We use this result and measurements of the rate of tunneling between topological charge sectors to calculate the scaling behavior of the autocorrelation times of these observables on periodic and open lattices. There is a characteristic lattice spacing at which open boundary conditions become worthwhile for reducing autocorrelations and we show how this lattice spacing is related to the diffusion coefficient, the tunneling rate, and the lattice Euclidean time extent.

arXiv comment36 pages, 14 figures

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Cited by in corpus (14)

• Equivariant flow-based sampling for lattice gauge theory
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Topological critical slowing down: variations on a toy model
• Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
• Uncertainty Quantification in Lattice QCD Calculations for Nuclear Physics
• The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours
• Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants
• Lattice QCD on Non-Orientable Manifolds
• Background field method in the gradient flow
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Testing algorithms for critical slowing down
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Investigating some technical improvements to glueball calculations