标题： 用对称多探测方法评估拓扑电荷密度 显示英文标题

标题： Evaluating topological charge density with symmetric multi-probing method

摘要： 我们通过使用对称多探测(SMP)方法并采用3个模式来计算重叠狄拉克矩阵的迹，评估了格点上SU(3)规范场的拓扑电荷密度。 由于给定格点构型的拓扑电荷$Q$必须是一个整数，因此很容易估计系统误差（$Q$与最近整数的偏差）。 结果表明，与使用点源相比，使用SMP源在计算具有局域性的大型稀疏矩阵的逆矩阵的迹时表现出更高的效率和准确性。 我们还展示了误差与探测方案参数$r_{\mathrm{min}}$以及格点体积$N_{L}$和格点间距$a$之间的相关性。 发现使用SMP源计算迹时的计算时间比使用点源计算时对$N_{L}$的依赖性更小。 因此，SMP方法非常适合在大格点上进行计算。 显示英文摘要

摘要： 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 $r_{\mathrm{min}}$ 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.