Algorithms for lattice QCD and related models

晶格QCD算法及相关模型

基本信息

批准号：
321114788
负责人：
Dr. Martin Herbert Hasenbusch
金额：
--
依托单位：
Institut für Theoretische Physik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2018-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/321114788?language=en
关键词：
Algorithms lattice QCD related models

项目摘要

Lattice QCD is the standard method for the theoretical study of strong interactions beyond perturbation theory. Quantitative results for hadronic properties are usually obtained from Monte Carlo simulations. The numerical task is however challenging. In particular the proper treatment of sea quarks is demanding. Nethertheless, in the four decades of its existance it matured and today allows us to compute many observables of interest to QCD phenomenology to good accuracy. Technical progress in lattice QCD has been driven from the increase of computational power and advances in algorithms. In this proposal we focus on the latter.In the last two decades, there has been much progress in the treatment of dynamical sea quarks. Large scale simulations rely on the representation of the fermion determinant by an integral over auxiliary fields. In its simplest form, this idea goes back to Petcher and Weingarten in 1981. The standard algorithm is the Hybrid Monte Carlo (HMC) algorithm proposed by Duane et al. in 1987. For the implementation used until about 2000, the numerical effort increased strongly with decreasing fermion mass. As a result, the masses that could be reached were far too large compared with those of the up and down quarks. Since then, the situation has been much improved by solvers that show a better behavior with decreasing fermion mass and by less noisy integral representations of the fermion determinant. The simplest of these is the mass preconditioning introduced in 1999 by myself. Similar in spirit is the domain decomposition (DD) HMC algorithm proposed by Lüscher. Here we shall exploit the idea of domain decomposition in temporal direction only. In particular we shall put domain decomposition on top of even/odd preconditioning. Further motivation for the domain decomposition in temporal only comes from the proposal of Ce, Giusti and Schaefer for a variance reduced estimator for fermionic correlation functions. With such estimators one is, for example, aiming at more accurate and reliable estimates of baryon masses. In lattice QCD one finds severe slowing down due to barriers between sectors of different topological charge. Lüscher proposed to overcome this problem by replacing periodic by open boundary conditions in temporal direction. Here we shall investigate parallel tempering, using different tempering parameters.Most Monte Carlo algorithms that are used to simulate spin models and lattice field theories today fulfill detailed balance. This enshures stabilty of the Markov chain. Recently it has been demonstrated for simple spin models that abandoning detailed balance, while keeping stability of course, considerable performance gains can be achieved. In the proposed project we like to push these ideas in the direction of lattice QCD. As a first step we shall implement the so called event driven Monte Carlo for princible chiral models. Within our project, we are aiming at the pure SU(3) gauge model.

格子 QCD 是强相互作用理论研究的标准方法，但强子性质的定量结果通常是通过蒙特卡罗模拟获得的，但对海夸克的正确处理要求很高。在它存在的四十年里，它已经成熟，今天使我们能够以良好的精度计算 QCD 现象学感兴趣的许多观测值。格子 QCD 的技术进步是由它的增长推动的。在过去的二十年中，动态海夸克的处理依赖于积分表示的费米子行列式，取得了很大进展。这个想法最简单的形式可以追溯到 1981 年的 Petcher 和 Weingarten。标准算法是 Duane 等人于 1987 年提出的混合蒙特卡罗 (HMC) 算法。对于2000年左右使用的实现，随着费米子质量的急剧下降，数值工作量增加，因此，与上夸克和下夸克相比，可以达到的质量太大了。通过解算器通过降低费米子质量和噪声较小的费米子行列式积分表示来改进，其中最简单的是我自己在 1999 年引入的质量预处理，其精神类似。 Lüscher 提出的域分解（DD）HMC 算法在这里我们将仅利用时间方向上的域分解的思想，特别是我们将域分解置于偶数/奇数预处理之上。时间仅来自 Ce、Giusti 和 Schaefer 对费米子相关函数的方差减少估计器的提议，例如，使用此类估计器的目的是更准确且更可靠地估计重子质量。在晶格 QCD 中，由于不同拓扑电荷扇区之间的势垒，我们发现了严重的减慢，Lüscher 提出通过在时间方向上用开放边界条件替换周期性来克服这一问题。这里我们将使用不同的回火参数来研究平行回火。如今用于模拟自旋模型和晶格场论的算法可以确保马尔可夫链的稳定性，最近它已经被证明可以放弃详细平衡，同时保持稳定性。在所提出的项目中，我们希望将这些想法推向晶格 QCD 的方向，作为第一步，我们将在我们的项目中实现所谓的事件驱动蒙特卡罗。纯 SU(3) 规范模型。