Evaluating topological charge density with symmetric multi-probing method

Abstract

We evaluated the topological charge density of SU(3) gauge fields on lattice by calculating the trace of overlap Dirac matrix employing symmetric multi-probing(SMP) method with 3 modes. Since the topological charge $Q$ for a given lattice configuration must be an integer number, it's easy to estimate the systematic error (the deviation of $Q$ to nearest integer). The results showed high efficiency and accuracy in calculating the trace of the inverse of a large sparse matrix with locality by using SMP sources, compared with that using point sources. We also showed the correlation between the errors and probing scheme parameter $r_{\min }$ as well as lattice volume $N_L$ and lattice spacing $a$. It was found that the computing time of calculating the trace by employing SMP sources is less dependent on $N_L$ than that by using point sources. Therefore the SMP method is very suitable for calculations on large lattices.

arXiv comment11 pages, 11 figures, to be published in Chinese Physics C

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• Exactly massless quarks on the lattice
• More about exactly massless quarks on the lattice
• Locality properties of Neuberger's lattice Dirac operator
• Exact chiral symmetry, topological charge and related topics
• Exploring the structure of the quenched QCD vacuum with overlap fermions
• On the Local Structure of Topological Charge Fluctuations in QCD
• Chiral properties of domain-wall quarks in quenched QCD
• Chiral Logs in Quenched QCD
• Variance reduction with practical all-to-all lattice propagators
• Exploring the role of the charm quark in the $\Delta I=1/2$ rule

Cited by in corpus (1)

• The dependence of overlap topological charge density on Wilson mass parameter