An iterative method to compute the overlap Dirac operator at nonzero chemical potential
arXiv:0710.0341 · doi:10.1016/j.cpc.2007.07.012
Abstract
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.
7 pages, talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany
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Cited by in corpus (9)
- Domain-wall and overlap fermions at nonzero quark chemical potential
- Restarted Hessenberg method for solving shifted nonsymmetric linear systems
- A nested Krylov subspace method to compute the sign function of large complex matrices
- Short-recurrence Krylov subspace methods for the overlap Dirac operator at nonzero chemical potential
- Large Wilson loops with overlap and clover fermions: Two-loop evaluation of the b-quark mass shift and the quark-antiquark potential
- A numerical method to compute derivatives of functions of large complex matrices and its application to the overlap Dirac operator at finite chemical potential
- A Method to Calculate Conserved Currents and Fermionic Force for the Lanczos Approximation to the Overlap Dirac Operator
- A SQMRCGstab Algorithm for Families of Shifted Linear Systems
- A method to compute derivatives of functions of large complex matrices