Who: Patrick Oare from Brookhaven National Laboratory
When: Monday, May 4, 2:10pm
Where: Theory Center, Pupin 8th Floor
Title: Non-Hermitian Eigensolvers for Lattice Gauge Theory
Abstract: 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. In this talk, I will discuss the application of eigensolver algorithms to non-Hermitian Dirac operators. I will present the first application of the harmonic Krylov-Schur algorithm to lattice gauge theory, which can be better access eigenvalues deep inside the spectrum of the Dirac operator. I will demonstrate a link between the harmonic Krylov-Schur algorithm and existing spectral flow methods that are used to understand the real eigenmodes of the Wilson-Dirac operator. Finally, I will show numerical results from harmonic Krylov-Schur that directly reveal topological sector changes across different gauge field configurations.
