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Numerical methods for the QCD overlap operator IV: Hybrid Monte Carlo

机译：QCD重叠算子的数值方法IV：混合蒙特卡洛

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摘要

The computational costs of calculating the matrix sign function of the overlap operator together with fundamental numerical problems related to the discontinuity of the sign function in the kernel eigenvalues are the major obstacle towards simulations with dynamical overlap fermions using the Hybrid Monte Carlo algorithm. In a previous paper of the present series we introduced optimal numerical approximation of the sign function and have developed highly advanced preconditioning and relaxation techniques which speed up the inversion of the overlap operator by nearly an order of magnitude. In this fourth paper of the series we construct an HMC algorithm for overlap fermions. We approximate the matrix sign function using the Zolotarev rational approximation, treating the smallest eigenvalues of the Wilson operator exactly within the fermionic force. Based on this we derive the fermionic force for the overlap operator. We explicitly solve the problem of the Dirac delta-function terms arising through zero crossings of eigenvalues of the Wilson operator. The main advantage of scheme is that its energy violations scale better than O(Delta tau(2)) and thus are comparable with the violations of the standard leapfrog algorithm over the course of a trajectory. We explicitly prove that our algorithm satisfies reversibility and area conservation. We present test results from our algorithm on 4(4), 6(4), and 8(4) lattices. (C) 2008 Elsevier B.V. All rights reserved.
机译：计算重叠算子的矩阵符号函数的计算成本以及与内核特征值中符号函数的不连续性相关的基本数值问题，是使用混合蒙特卡罗算法进行动态重叠费米子仿真的主要障碍。在本系列的前一篇文章中，我们介绍了符号函数的最佳数值逼近，并开发了高度先进的预处理和松弛技术，该技术将重叠算子的反转速度提高了近一个数量级。在该系列的第四篇文章中，我们构造了重叠费米子的HMC算法。我们使用Zolotarev有理逼近来近似矩阵符号函数，恰好在铁离子力内处理了Wilson算子的最小特征值。基于此，我们推导了重叠算符的费米力。我们显式地解决了威尔逊算子的特征值过零导致的狄拉克三角函数项的问题。该方案的主要优点是它的能量违规比O（Delta tau（2））更好，因此在轨迹过程中可以与标准跨越式算法的违规相比。我们明确证明了我们的算法满足可逆性和面积守恒。我们在4（4），6（4）和8（4）格上展示了我们算法的测试结果。 （C）2008 Elsevier B.V.保留所有权利。

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