A Method to Calculate Conserved Currents and Fermionic Force for the Lanczos Approximation to the Overlap Dirac Operator

TL;DR

This paper introduces a method for efficiently computing the overlap Dirac operator and its derivatives, facilitating calculations of conserved currents and fermionic forces in lattice QCD simulations.

Contribution

A novel approach to simultaneously compute the overlap operator and its derivatives, improving efficiency in lattice QCD computations.

Findings

Enables efficient calculation of conserved currents.

Facilitates fermionic force evaluation in HMC.

Reduces computational cost of overlap operator derivatives.

Abstract

The overlap Dirac operator obeys the Ginsparg-Wilson equation and offers a possibility to introduce chiral symmetry on the lattice. Evaluating the overlap operator is numerically very expensive and one has to rely on approximation methods. At finite chemical potential the overlap operator can be efficiently computed with the two-sided Lanczos algorithm. To calculate conserved currents on the lattice, or to evaluate the fermionic force in HMC calculations, one needs to compute derivatives of the Dirac operator with respect to gauge fields. In this paper we present a method to simultaneously compute the action of the overlap operator and its derivative on a source vector.