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通过蒙特卡罗模拟得到。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需要的。然而，在它存在的40年里，它成熟了，今天我们可以很准确地计算许多对QCD现象学感兴趣的观测值。晶格QCD的技术进步是由计算能力的提高和算法的进步驱动的。在本建议中，我们着重于后者。在过去的二十年里，在动力学海夸克的处理方面取得了很大的进展。大规模模拟依赖于费米子行列式在辅助场上的积分表示。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1987年Duane等人提出的混合蒙特卡罗（Hybrid Monte Carlo， HMC）算法。直到2000年，数值上的努力随着费米子质量的减少而增加。结果，与上下夸克的质量相比，可以达到的质量太大了。从那时起，由于求解器在费米子质量下降时表现出更好的行为，以及费米子行列式的较少噪声的积分表示，情况得到了很大的改善。其中最简单的是我在1999年提出的大规模预处理。在精神上类似的是l<s:1> scher提出的域分解（DD） HMC算法。这里我们将只在时间方向上利用区域分解的思想。特别地，我们将把域分解放在偶/奇预处理之上。进一步的时域区域分解的动机来自Ce， Giusti和Schaefer对费米子相关函数方差减少估计量的提出。例如，有了这样的估计器，人们的目标是更准确、更可靠地估计重子的质量。在晶格QCD中，人们发现由于不同拓扑电荷扇区之间的障碍导致了严重的减速。l<s:2> scher提出在时间方向上用开边界条件代替周期条件来克服这一问题。这里我们将研究平行回火，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。这保证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，放弃详细的平衡，同时保持稳定的过程，可以获得相当大的性能增益。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，我们将实现所谓的事件驱动蒙特卡罗原理手性模型。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.