Related papers: The Overlap Dirac Operator
We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma_5-hermitian, but its nonreal eigenvalues still…
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 perform a comparative study of the infrared properties of overlap and staggered fermions in QCD. We observe that the infrared spectrum of the APE/HYP improved staggered Dirac operator develops a four-fold near-degeneracy and is in…
An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The overlap number of a graph is the minimum number of elements…
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 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…
A numerical investigation of the quenched Schwinger model on the lattice using the overlap Dirac operator points to a divergent chiral condensate.
We discuss the weak coupling expansion of lattice QCD with the overlap Dirac operator. The Feynman rules for lattice QCD with the overlap Dirac operator are derived and the quark self-energy and vacuum polarization are studied at 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…
We analyze the limit of the spectrum of a geometric Dirac-type operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the…
Introduction of supersymmetry into the noncommutative geometry is investigated. We propose a new Dirac operator which plays the role of the metric over the extended algebra of chiral and antichiral supermultiplets and is invariant under the…
In this note we present some properties of the Dirac operator on noncompact metric graphs with Kirchoff-type vertex conditions. In particular, we discuss the specific features of the spectrum of the operator and, finally, we give some…
We apply the topology conserving gauge action proposed by Luescher to the four-dimensional lattice QCD simulation in the quenched approximation. With this gauge action the topological charge is stabilized along the hybrid Monte Carlo…
We define a sparse hermitian lattice Dirac matrix, $H$, coupling $2n+1$ Dirac fermions. When $2n$ fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We…
We review a procedure of factorizing the Minkowski space Dirac operator over a~suitable superspace, discuss its Euclidean space version and apply the worked out formalism in the case od an almost-commutative Dirac operator. The presented…
We compute the one-loop lattice renormalization of the two-quark operators $\bar{\psi} \Gamma \psi$, where $\Gamma$ denotes the generic Dirac matrix, for the lattice formulation of QCD using the overlap-Dirac operator. We also study the…
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…
We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for…
We compute the ratio between the scale $\Lambda_L$ associated with a lattice formulation of QCD using the overlap-Dirac operator, and $\Lambda_{MS-bar}$. To this end, the one-loop relation between the lattice coupling $g_0$ and the coupling…
We evaluate for arbitrary even dimensions the classical continuum limit of the lattice axial anomaly defined by the overlap-Dirac operator. Our calculational scheme is simple and systematic. In particular, a powerful topological argument is…