The overlap 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, which benefits dynamical overlap fermion simulations.

Contribution

The paper presents a novel five-dimensional formulation of the overlap operator based on continued fractions, improving computational efficiency and conditioning for dynamical fermion simulations.

Findings

Inverse of the overlap operator can be computed via a single Krylov space method.

The five-dimensional linear system can be well conditioned through equivalence transformations.

The approach enhances efficiency in simulating dynamical overlap fermions.

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 where nested conjugate gradient procedures are avoided. We show that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions. This is of significant importance when dynamical overlap fermions are simulated.