arXiv 2009.010292020-09-02hep-lat

格点量子色动力学中构造关联函数的场稀疏化

Field sparsening for the construction of the correlation functions in lattice QCD

Yuan Li, Shi-Cheng Xia, Xu Feng, Lu-Chang Jin, Chuan Liu

备注：: 16 pages, 9 figures
发表信息：: Phys. Rev. D 103, 014514 (2021)
DOI：: 10.1103/PhysRevD.103.014514

摘要：

本文采用两种场稀疏化方法，即稀疏网格法和随机场选择法，构造了格点量子色动力学中的两点和三点关联函数。我们认为，由于在与源，电流和汇位置相关的不同场点的晶格常数之间的高相关性，可以节省大量的计算时间，通过在晶格位点的子集上执行求和。此外，使用这种策略，只需要存储一小部分完整的夸克传播子。结果表明，对于点源算子，场点数可减少$\sim$ 100倍，对于高斯涂抹算子，场点数可减少$\sim$ 1000倍，而修正算子的不确定度仅增加$\sim$ 15%.因此，以适度的计算资源的成本，人们可以接近的精度的所有到所有使用字段稀疏的方法。

英文摘要：

Two field-sparsening methods, namely the sparse-grid method and the random field selection method, are used in this paper for the construction of the 2-point and 3-point correlation functions in lattice QCD. We argue that, due to the high correlation among the lattice correlators at different field points associated with source, current, and sink locations, one can save a lot of computational time by performing the summation over a subset of the lattice sites. Furthermore, with this strategy, one only needs to store a small fraction of the full quark propagators. It is found that the number of field points can be reduced by a factor of $\sim$100 for the point-source operator and a factor of $\sim$1000 for the Gaussian-smeared operator, while the uncertainties of the correlators only increase by $\sim$15\%. Therefore, with a modest cost of the computational resources, one can approach the precision of the all-to-all correlators using the field-sparsening methods.

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