Evaluating the topological charge density with the symmetric multi-probing method

Abstract

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

Dependence of overlap topological charge density on Wilson mass parameter *

“…in the calculation of topological charge density [14,15], which makes the computation on the large lattice almost impossible. To reduce the computational cost, the symmetric multi-probing source (SMP) method is introduced to calculate the topological charge density [16].…”