论文标题
手性晶格费米斯的跨部：域墙
Multigrid for Chiral Lattice Fermions: Domain Wall
论文作者
论文摘要
Krylov Dirac求解器的批判放慢速度为晶格场理论进一步进步时，这是一个主要的障碍，它接近连续解决方案。我们为手性费米子提出了一种新的多机疗法方法，适用于5-D域壁或4-D重叠操作员。核心思想是直接使4-D Wilson内核磨损，在每个级别上给出有效的域墙或重叠操作员。我们在这里为Shamir域壁配方提供了明确的结构，并为2-D Schwinger原型进行了数值测试，展示了接近理想的多网格缩放。该框架是为4-D晶格QCD手性费米子的自然扩展而设计的，例如Möbius，Zolotarev或Borici域壁离散，或直接用于4-D重叠操作员的合理扩展。对于Shamir操作员，通过在最近交错的MG算法中使用的Kähler-Dirac频谱图的精神使用Pauli-Villars预处理的有效重叠操作员可以隔离。
Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both the 5-d domain wall or 4-d Overlap operator. The central idea is to directly coarsen the 4-d Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2-d Schwinger prototype, demonstrating near ideal multi-grid scaling. The framework is designed for a natural extension to 4-d lattice QCD chiral fermions, such as the Möbius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4-d Overlap operator. For the Shamir operator, the effective overlap operator is isolated by the use of a Pauli-Villars preconditioner in the spirit of the Kähler-Dirac spectral map used in a recent staggered MG algorithm [1].
