出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：The overlap Dirac operator at nonzero quark chemical potential involves the computation of the
sign function of a non-Hermitian matrix. In this talk we present an iterative method, first proposed
by us in Ref. [1], which allows for an efficient computation of the operator, even on large lattices.
The starting point is a Krylov subspace approximation, based on the Arnoldi algorithm, for the
evaluation of a generic matrix function. The efficiency of this method is spoiled when the matrix
has eigenvalues close to a function discontinuity. To cure this, a small number of critical eigenvectors
are added to the Krylov subspace, and two different deflation schemes are proposed in this
augmented subspace. The ensuing method is then applied to the sign function of the overlap Dirac
operator, for two different lattice sizes. The sign function has a discontinuity along the imaginary
axis, and the numerical results show how deflation dramatically improves the efficiency of the
method.
