Related papers: The overlap operator as a continued fraction
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…
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…
We derive the vector-like four dimensional overlap Dirac operator starting from a five dimensional Dirac action in the presence of a delta-function space-time defect. The effective operator is obtained by first integrating out all the…
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…
We present a novel method to compute the overlap Dirac operator at zero and nonzero quark chemical potential. To approximate the sign function of large, sparse matrices, standard methods project the operator on a much smaller Krylov…
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…
A practical implementation of the Overlap-Dirac operator ${{1+\gamma_5\epsilon(H)}\over 2}$ is presented. The implementation exploits the sparseness of $H$ and does not require full storage. A simple application to parity invariant three…
I derive the overlap Dirac operator starting from the overlap formalism, discuss the numerical hurdles in dealing with this operator and present ways to overcome them.
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.…
We study three practical implementations of the Overlap-Dirac operator $D_o= (1/2) [1 + \gamma_5\epsilon(H_w)]$ in four dimensions. Two implementations are based on different representations of $\epsilon(H_w)$ as a sum over poles. One of…
We have recently given a construction of the overlap Dirac operator at nonzero quark chemical potential. Here, we introduce a quark chemical potential in the domain-wall fermion formalism and show that our earlier result is reproduced if…
We propose new techniques for the numerical implementation of the overlap-Dirac operator, which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger…
A recently developed numerical method for the calculation of derivatives of functions of general complex matrices, which can also be combined with implicit matrix function approximations such as Krylov-Ritz type algorithms, is presented. An…
In this talk I propose a new computational scheme with overlap fermions and a fast algorithm to invert the corresponding Dirac operator.
This paper reviews the most popular methods which are used in lattice QCD to compute the determinant of the lattice Dirac operator: Gaussian integral representation and noisy methods. Both of them lead naturally to matrix function problems.…
The overlap Dirac operator in lattice QCD requires the computation of the sign function of a matrix. While this matrix is usually Hermitian, it becomes non-Hermitian in the presence of a quark chemical potential. We show how the action of…
We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the…
The overlap hypercube fermion is constructed by inserting a lattice fermion with hypercubic couplings into the overlap formula. One obtains an exact Ginsparg-Wilson fermion, which is more complicated than the standard overlap fermion, but…
The extreme computational costs of calculating the sign of the Wilson matrix within the overlap operator have so far prevented four dimensional dynamical overlap simulations on realistic lattice sizes, because the computational power…
We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular…