Speaker
Description
The Dirac operator is a fundamental object in lattice gauge theory. Its spectral properties carry direct physical significance: its low modes limit convergence in Krylov-based linear solvers, and real (zero) eigenvalues of the Wilson (overlap) Dirac operator correspond to topologically non-trivial field configurations. While the spectrum of Hermitian Dirac operators is real and easy to compute via the Lanczos algorithm, the complex spectrum of non-Hermitian Dirac operators is more difficult to understand. A particular challenge is computing the interior eigenmodes of non-Hermitian Dirac operators, which are naturally suppressed in Krylov-based methods. In this talk, I will present the first application of the Krylov-Schur eigenvalue algorithm to lattice gauge theory. Its harmonic extension can be used to access interior eigenmodes of non-Hermitian Dirac operators. I will contrast the Krylov-Schur algorithm with the standard Arnoldi iteration, and discuss an application of how the Krylov-Schur algorithm may be used better understand the convergence of multigrid solvers.