多个含不同质量项的费米子矩阵求逆算法

Inversion algorithm for fermion matrix with multi-different mass terms

在格点量子色动力学的模拟中,Rational Hybrid Monte Carlo (RHMC)算法是一种精确的,能应用到任意多个味道数的费米子的方法.它的思想是把费米子行列式展开为有理函数的形式.但该方法会带来很多彼此相差一个常对角矩阵的矩阵的求逆的计算,消耗大量的时间和计算资源,限制了RHMC算法的应用.本文利用移位多项式,针对共轭梯度法得到多个含有不同质量项的矩阵求逆的一种方法,该方法可以应用到RHMC算法中.

In the simulation of lattice gauge theory, RHMC algorithm is an accurate algorithm which can be used to any number of fermions. Its central idea is to expand the fermion determinant into rational functions, the implementation of this algorithm results in a lot of matrix inversion of fermion matrix, and brings about numerous time and resources consumption. Therefore, its use is limited. This paper uses the shifted polynomial to obtain an approach to solve this problem for the conjugate gradient method. This approach can be applied into RHMC algorithm.