Acceleration of the Arnoldi method and real eigenvalues of the non-Hermitian WilsonDirac operator
In this paper, we present a method for the computation of the low-lying real eigenvalues of the WilsonDirac operator based on the Arnoldi algorithm. These eigenvalues contain information about several observables. We used them to calculate the sign of the fermion determinant in one-flavor QCD and the sign of the Pfaffian in N=1 N = 1 super YangMills theory. The method is based on polynomial transformations of the WilsonDirac operator, leading to considerable improvements of the computation of eigenvalues. We introduce an iterative procedure for the construction of the polynomials and demonstrate the improvement in the efficiency of the computation. In general, the method can be applied to operators with a symmetric and bounded eigenspectrum.
arnoldi algorithm super yangmills theory lattice qcd wilsondirac operator eigenvalues