Related papers: The overlap Dirac operator as a continued fraction

The overlap operator in lattice QCD requires the computation of the sign function of a matrix, which is non-Hermitian in the presence of a quark chemical potential. In previous work we introduced an Arnoldi-based Krylov subspace…

The overlap operator is a lattice discretization of the Dirac operator of quantum chromodynamics, the fundamental physical theory of the strong interaction between the quarks. As opposed to other discretizations it preserves the important…

It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge…

I present several tricks to help implement the overlap Dirac operator numerically.

Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks…

Using the overlap formulation, we calculate the fermionic determinant on the lattice for chiral fermions with twisted boundary conditions in two dimensions. When the lattice spacing tends to zero we recover the results of the usual…

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.…

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…

The Overlap-Dirac operator provides a lattice regularization of massless vector gauge theories with an exact chiral symmetry. Practical implementations of this operator and recent results in quenched QCD using this Overlap-Dirac operator…

In this talk I propose a new computational scheme with overlap fermions and a fast algorithm to invert the corresponding Dirac operator.

In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is…

Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form…

We show that, for each symmetry class based on the tenfold way classification, the effective Dirac operator obtained by integrating out the additional bulk direction takes a value in the corresponding classifying space, from which we obtain…

We compute fermionic observables relevant to the study of chiral symmetry in quenched QCD using the Overlap-Dirac operator for a wide range of the fermion mass. We use analytical results to disentangle the contribution from exact zero modes…

We review the spectral flow techniques for computing the index of the overlap Dirac operator including results relevant for SUSY Yang-Mills theories. We describe properties of the overlap Dirac operator, and methods to implement it…

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 action of the overlap-Dirac operator on a vector is typically implemented in directly through a multi-shift conjugate gradient solver. The compute-time this takes to evaluate depends upon the condition number $\kappa$ of the matrix that…

We present relaxation and preconditioning techniques which accelerate the inversion of the overlap operator by a factor of four on small lattices, with larger gains as the lattice size increases. These improvements can be used in both…

The overlap operator is just the simplest of a class of Dirac operators with an exact chiral symmetry. I demonstrate how a general class of chiral Dirac operators can be constructed, show that they have no fermion doublers and that they are…

Rational approximations of the matrix sign function lead to multishift methods. For non-Hermitian matrices long recurrences can cause storage problems, which can be circumvented with restarts. Together with deflation we obtain efficient…