Computational methods for the fermion determinant and the link between overlap and domain wall fermions

摘要

This paper reviews the most popular methods which are used in lattice QCD tocompute the determinant of the lattice Dirac operator: Gaussian integralrepresentation and noisy methods. Both of them lead naturally to matrixfunction problems. We review the most recent development in Krylov subspaceevaluation of matrix functions. The second part of the paper reviews the formalrelationship and algebraic structure of domain wall and overlap fermions. Wereview the multigrid algorithm to invert the overlap operator. It is describedhere as a preconditioned Jacobi iteration where the preconditioner is the Schurcomplement of a certain block of the truncated overlap matrix.