Algorithms for lattice QCD and related models

格点QCD是微扰理论之外强相互作用理论研究的标准方法。 强子性质的定量结果通常是通过蒙特卡罗模拟得到的。然而，数字任务具有挑战性。特别是对海夸克的适当处理是苛刻的。尽管如此，在它存在的四十年里，它已经成熟，今天允许我们以很好的精度计算QCD现象学感兴趣的许多可观测量。计算能力的提高和算法的改进推动了格点QCD的技术进步。在过去的二十年里，动力学海夸克的研究取得了很大的进展。大规模的模拟依赖于费米子行列式的辅助领域的积分表示。最简单的形式，这个想法可以追溯到1981年的Petcher和Weingarten。标准算法是Duane等人在1987年提出的混合蒙特卡罗（HMC）算法。对于直到2000年使用的实现，数值努力随着费米子质量的减少而强烈增加。因此，与上夸克和下夸克的质量相比，可以达到的质量太大了。从那时起，这种情况已经得到了很大的改善，解决方案，显示出更好的行为与减少费米子质量和费米子行列式的噪音积分表示。其中最简单的是我在1999年引入的质量预处理。Lüscher提出的区域分解（DD）HMC算法在精神上类似。这里我们将只在时间方向上利用区域分解的思想。特别地，我们将把区域分解放在偶/奇预处理之上。进一步的动机在时间上的区域分解只来自于Ce，Giusti和Schaefer的提案，用于费米子相关函数的方差减少估计。例如，使用这样的估计器，人们的目标是更准确和可靠地估计重子质量。在格点QCD中，人们发现由于不同拓扑荷的扇区之间的势垒而导致的严重的慢化。Lüscher提出通过在时间方向上用开边界条件代替周期性来克服这个问题。在这里，我们将研究平行回火，使用不同的回火参数。大多数蒙特卡罗算法，用于模拟自旋模型和晶格场理论今天实现详细的平衡。这保证了马尔可夫链的稳定性。最近的研究表明，对于简单的尾旋模型，在保持稳定性的同时，放弃详细的平衡，可以获得相当大的性能增益。在这个项目中，我们希望把这些想法推向格点QCD的方向。作为第一步，我们将实施所谓的事件驱动的蒙特卡罗原理手征模型。在我们的项目中，我们的目标是纯SU（3）规范模型。

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.