多项式滤波在质量预处理混合蒙特卡罗中的应用
Applying polynomial filtering to mass preconditioned Hybrid Monte Carlo
摘要：
在现代混合蒙特卡罗模拟中，质量预处理或Hasenbusch滤波的使用是常见的。在轻夸克质量下，通常使用多个滤波器（三个或更多）来降低产生动态规范场的成本;然而，调整大量哈森布施质量项的任务是不平凡的。使用短多项式近似的逆已被证明提供了一个有效的UV过滤器HMC模拟。在这项工作中，我们研究了多项式滤波的质量预处理的混合蒙特卡罗算法的应用，作为一种手段，引入许多时间尺度的分子动力学集成与简化的参数调整过程。本文还介绍了一种广义多尺度积分方法，它允许任意步长，并可应用于Omelyan型积分器。我们发现，多项式滤波质量预处理（PF-MP）执行以及或优于标准的质量预处理，与所需的微调显着减少。
英文摘要：
The use of mass preconditioning or Hasenbusch filtering in modern Hybrid Monte Carlo simulations is common. At light quark masses, multiple filters (three or more) are typically used to reduce the cost of generating dynamical gauge fields; however, the task of tuning a large number of Hasenbusch mass terms is non-trivial. The use of short polynomial approximations to the inverse has been shown to provide an effective UV filter for HMC simulations. In this work we investigate the application of polynomial filtering to the mass preconditioned Hybrid Monte Carlo algorithm as a means of introducing many time scales into the molecular dynamics integration with a simplified parameter tuning process. A generalized multi-scale integration scheme that permits arbitrary step- sizes and can be applied to Omelyan-style integrators is also introduced. We find that polynomial-filtered mass-preconditioning (PF-MP) performs as well as or better than standard mass preconditioning, with significantly less fine tuning required.
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