Related papers: On the Neuberger overlap operator

Eigenvalues of a Wilson loop operator are gauge invariant and their distribution undergoes a transition at infinite N as the size of the loop is changed. We study this transition using the average characteristic polynomial associated with…

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.

We compute exactly the overlap between the eigenvectors of two large empirical covariance matrices computed over intersecting time intervals, generalizing the results obtained previously for non-intersecting intervals. Our method relies on…

We measure the low lying eigenmodes of an overlap Dirac operator on 2--flavor staggered configurations. By comparing the eigenmode distribution to the predictions of Random Matrix Theory we test to what accuracy staggered configurations…

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 analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived…

The eigenvalue distribution of a Wilson loop operator of fixed shape undergoes a transition under scaling at infinite N. We derive a large N scaling function in a double scaling limit of the average characteristic polynomial associated with…

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…

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations…

We propose a continuous approach to computing the pseudospectra of linear operators with compact or compact-plus-scalar resolvent, following a 'solve-then-discretize' strategy. Instead of taking a finite section approach or using a…

The numerical and computational aspects of chiral fermions in lattice quantum chromodynamics are extremely demanding. In the overlap framework, the computation of the fermion propagator leads to a nested iteration where the matrix vector…

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's…

Using the overlap-Dirac operator proposed by Neuberger, we have computed in lattice QCD the one-loop renormalization factors of ten operators which measure the lowest two moments of unpolarized and polarized non-singlet quark distributions.…

We calculate the chiral condensate of QCD with 2, 2+1 and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up and down quark masses covering a range between 3 and 100 MeV. On L ~…

Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields…

We establish an upper estimate for the small eigenvalues of the twisted Dirac operator on Kahler submanifolds in Kahler manifolds carrying Kahlerian Killing spinors. We then compute the spectrum of the twisted Dirac operator of the…

A numerical investigation of the quenched Schwinger model on the lattice using the overlap Dirac operator points to a divergent chiral condensate.

Numerical experiments on most gauge theories coupled with matter failed to observe string-breaking effects while measuring Wilson loops only. We show that, under rather mild assumptions, the overlap of the Wilson loop operator with the…

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 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…