用全模平均和区域分解求解器计算格点量子色动力学的核子矩阵元：探索性研究
Nucleon matrix elements from lattice QCD with all-mode-averaging and a domain-decomposed solver: an exploratory study
摘要：
我们研究了与局部放气的SAP预处理求解器结合使用时的全模式平均（AMA）的性能，确定如何优化局部块大小和放气字段的数量，以最大限度地减少给定水平的整体统计精度的计算成本。我们发现，AMA能够减少核子电荷的统计误差的一个因素，在相同的成本相比，标准的方法。作为演示，我们计算了具有非微扰O（a）改进的Wilson夸克的$N_f=2$格点量子色动力学中核子的轴荷、标量荷和张量荷，使用O（10，000）测量追踪信号到$t_s\sim 1.5$ fm的源-汇分离。我们的研究结果表明，轴向电荷是从一个显着的量（5-10%）的激发态污染源-汇分离高达$t_s\sim 1.2$ fm，而标量和张量电荷的激发态污染似乎很小。
英文摘要：
We study the performance of all-mode-averaging (AMA) when used in conjunction with a locally deflated SAP-preconditioned solver, determining how to optimize the local block sizes and number of deflation fields in order to minimize the computational cost for a given level of overall statistical accuracy. We find that AMA enables a reduction of the statistical error on nucleon charges by a factor of around two at the same cost when compared to the standard method. As a demonstration, we compute the axial, scalar and tensor charges of the nucleon in $N_f=2$ lattice QCD with non-perturbatively O(a)-improved Wilson quarks, using O(10,000) measurements to pursue the signal out to source-sink separations of $t_s\sim 1.5$ fm. Our results suggest that the axial charge is suffering from a significant amount (5-10%) of excited-state contamination at source-sink separations of up to $t_s\sim 1.2$ fm, whereas the excited-state contamination in the scalar and tensor charges seems to be small.
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