The overlap Dirac operator as a continued fraction

TL;DR

This paper introduces a five-dimensional formulation of the overlap lattice Dirac operator using continued fraction expansion, enabling efficient computation of its inverse without nested conjugate gradient procedures.

Contribution

It presents a novel five-dimensional approach to the overlap Dirac operator that simplifies inverse calculations and improves conditioning via continued fractions.

Findings

Inverse of the overlap operator computed with a single Krylov space method

Avoidance of nested conjugate gradient procedures

Enhanced conditioning of the linear system through equivalence transformations

Abstract

We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method and nested conjugate gradient procedures are avoided. We point out that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions.