Diffusion of topological charge in lattice QCD simulations

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 th...

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Bibliographic Details
Published in:arXiv.org 2014-06
Main Authors: McGlynn, Greg, Mawhinney, Robert D
Format: Article
Language:English
Subjects:
Autocorrelation functions
Boundary conditions
Charge density
Computer simulation
Diffusion coefficient
Diffusion rate
Gauge theory
Lattice theory
Lattices
Mathematical analysis
Quantum chromodynamics
Topology
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1406.4551