Related papers: On the Neuberger overlap operator
In a system where chiral symmetry is spontaneously broken, the low energy eigenmodes of the continuum Dirac operator are extended. On the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes that affect…
We study the spectrum of the hermitian Wilson Dirac operator in the epsilon-regime of QCD in the quenched approximation and compare it to predictions from Wilson Random Matrix Theory. Using the distributions of single eigenvalues in the…
We investigate optimal choices for the (outer) iteration method to use when solving linear systems with Neuberger's overlap operator in QCD. Different formulations for this operator give rise to different iterative solvers, which are…
The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at…
We use low lying eigenvectors of the overlap-Dirac operator as a probe of the QCD vacuum. If instantons play a significant role one would expect the low lying eigenmodes of the overlap-Dirac operator to consist mainly of the mixed ``would…
We determine the free field hypercubic Dirac operator which is optimally close to satisfying the Ginsparg-Wilson relation. Inserting this operator into the overlap formula, we show that the analytic locality bound on the resulting overlap…
We report on our progress in using the overlap-Dirac fermion operator in simulations of lattice QCD. We have investigated the Lanczos based method of Borici, as well as various rational approximations, to calculate the step function in the…
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…
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…
This thesis is dedicated to explore the feasibility of numerical calculations in the $\epsilon$--regime of QCD for the extraction of physical information. We apply two formulations of the Ginsparg-Wilson fermions the Neuberger operator and…
We propose a practical formulation of the overlap Dirac operator in lattice QCD that employs the diagonal Kenney-Laub rational iterates - expressed via their partial fraction decomposition - to approximate the matrix sign function. We…
We outline our implementation of the adaptive thick-restart Lanczos algorithm ($a$-TRLan) for the projection of the low-lying eigenmodes of the overlap Dirac operator in lattice QCD, and compare the performances of our code and the widely…
Some key features of the overlap operator with a UV-filtered Wilson kernel are discussed. The first part concerns spectral properties of the underlying shifted hermitean Wilson operator and the relation to the observed speedup of the…
We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix…
We describe in some detail our numerical treatment of Neuberger's lattice Dirac operator as implemented in a practical application. We discuss the improvements we have found to accelerate the numerical computations and give an estimate of…
The spectral properties of the Wilson-Dirac operator in 2-dimensional QED responsible for the appearance of exceptional configurations in quenched simulations are studied in detail. The mass singularity structure of the quenched functional…
We summarize our recent investigations of lattice QCD with dynamical overlap fermions. We sketch algorithmic issues and our approach to solving them. We show our measurement of the topological susceptibility. We describe a computation of…
It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An…
Two numerical algorithms for the computation of eigenvalues of Dirac operators in lattice gauge theories are described: one is an accelerated conjugate gradient method, the other one a standard Lanczos method. Results obtained by Cullum's…
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 an iterative method, first proposed by us in Ref. [1], which allows for an…