Related papers: On the Spectrum of Lattice Dirac Operators
Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed…
We study the spectrum properties for a recently constructed fixed point lattice Dirac operator. We also consider the problem of the extraction of the fermion condensate, both by direct computation, and through the Banks-Casher formula by…
We review the exact results for microscopic Dirac operator spectra based on either Random Matrix Theory, or, equivalently, chiral Lagrangians. Implications for lattice calculations are discussed.
We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action…
We present a numerical study of the properties of the Fixed Point lattice Dirac operator in the Schwinger model. We verify the theoretical bounds on the spectrum, the existence of exact zero modes with definite chirality, and the Index…
We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our…
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…
We compare the lower edge spectral fluctuations of the staggered lattice Dirac operator for the Schwinger model with the predictions of chiral Random Matrix Theory (chRMT). We verify their range of applicability, checking in particular the…
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…
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 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…
We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields.…
We investigate the interplay between topological charge and the spectrum of the fermion matrix in lattice-QED_2 using analytic methods and Monte Carlo simulations with dynamical fermions. A new theorem on the spectral decomposition of the…
We only require generalized chiral symmetry and $\gamma_5$-hermiticity, which leads to a large class of Dirac operators describing massless fermions on the lattice, and use this framework to give an overview of developments in this field.…
It has been shown recently that Dirac operators satisfying the Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at finite lattice spacing. We discuss different ways to construct these operators and their…
The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties…
We examine spectra of Dirac operators on compact hyperbolic surfaces. Particular attention is devoted to symmetry considerations, leading to non-trivial multiplicities of eigenvalues. The relation to spectra of Maass-Laplace operators is…
This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions…
Spectral properties of Schr\"odinger operators on compact metric graphs are studied and special emphasis is put on differences in the spectral behavior between different classes of vertex conditions. We survey recent results especially for…
Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac operator in a well-defined finite-volume scaling regime.