Algorithms for lattice QCD and related models

晶格QCD是超越微扰理论的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，数字任务是具有挑战性的。特别是，对海夸克的适当处理是非常苛刻的。然而，在它存在的40年里，它已经成熟了，今天它允许我们以很高的精度计算许多QCD现象学感兴趣的观测数据。计算能力的提高和算法的进步推动了格子QCD的技术进步。在这项提议中，我们将重点放在后者。在过去的二十年里，在动力海夸克的治疗方面取得了很大的进展。大规模模拟依赖于用辅助场上的积分来表示费米子行列式。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等人提出的混合蒙特卡罗(HMC)算法。1987年。对于一直使用到2000年的实现，数值计算的工作量随着费米子质量的减小而显著增加。结果，与上夸克和下夸克相比，可以到达的质量太大了。从那时起，随着费米子质量的减少和费米子行列式的低噪音积分表示，这种情况得到了很大的改善，表现出了更好的行为。其中最简单的是我在1999年引入的大规模预适应。与之类似的是L提出的区域分解(DD)HMC算法。在这里，我们将仅在时间方向上利用区域分解的思想。特别是，我们将把区域分解放在偶数/奇数预条件的顶部。在时间上区域分解的进一步动机仅来自于Ce，Giusti和Schaefer提出的费米子关联函数的方差减少估计器。例如，对于这样的估计器，人们的目标是对重子质量进行更准确和可靠的估计。在晶格QCD中，人们发现由于不同拓扑电荷的扇区之间的势垒，导致了严重的减速。L提出用时间方向的开边界条件代替周期边界条件来克服这一问题。在这里，我们将研究并行回火，使用不同的回火参数。目前用于模拟自旋模型和晶格场理论的大多数蒙特卡罗算法都实现了详细的平衡。这加强了马尔可夫链的稳定性。最近已经证明，对于简单的自旋模型，放弃了详细的平衡，当然，在保持稳定性的同时，可以获得相当大的性能收益。在提议的项目中，我们希望将这些想法推向晶格QCD的方向。作为第一步，我们将为原则性手征模型实现所谓的事件驱动蒙特卡罗。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.