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An iterative method to compute the overlap Dirac operator at nonzero chemical potential

Presenter: Jacques Bloch — University of Regensburg

Jacques Bloch and Tilo Wettig

Recently we extended the definition of the overlap Dirac operator to nonzero quark chemical potential, and showed that its microscopic spectral density agrees with the predictions of non-Hermitian chiral random matrix theory for trivial and non-trivial topologies. Here we give further evidence for the validity of this definition by showing that it corresponds to the domain-wall fermion formalism at nonzero chemical potential in the limit where the extent of the fifth dimension is taken to infinity. We then present an iterative method which allows for an efficient computation of the operator, even on large lattices. The new operator involves the sign of a non-Hermitian matrix, which is computed with a Krylov subspace approximation based on the Arnoldi algorithm. An important ingredient of the algorithm is the explicit treatment of eigenvalues close to the imaginary axis where the sign function is discontinuous.