Comparing iterative methods to compute the overlap Dirac operator at nonzero chemical potential

TL;DR

This paper compares iterative Krylov subspace methods, specifically Arnoldi and two-sided Lanczos, for efficiently computing the overlap Dirac operator at nonzero chemical potential in lattice QCD.

Contribution

It introduces and evaluates Krylov subspace approximations with eigenvalue deflation for large lattice computations, highlighting the efficiency of the two-sided Lanczos method.

Findings

Two-sided Lanczos method is faster and more effective than Arnoldi for this application.

Deflation of critical eigenvalues improves approximation accuracy.

The methods enable computations on large lattice sizes.

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 iterative Krylov subspace approximations, with deflation of critical eigenvalues, which we developed to compute the operator on large lattices. We compare the accuracy and efficiency of two alternative approximations based on the Arnoldi and on the two-sided Lanczos method. The short recurrences used in the latter method make it faster and more effective for realistic lattice simulations.