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Related papers: Low-Lying Eigenvalues of the Wilson-Dirac Operator

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Chiral perturbation theory for eigenvalue distributions, and equivalently random matrix theory, has recently been extended to include lattice effects for Wilson fermions. We test the predictions by comparison to eigenvalue distributions of…

High Energy Physics - Lattice · Physics 2013-01-15 Poul H. Damgaard , Urs M. Heller , Kim Splittorff

We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with…

High Energy Physics - Lattice · Physics 2007-05-23 Christof Gattringer , Stefan Solbrig

Finding the eigenvalues connected to the covariance operator of a centred Hilbert-space valued Gaussian process is genuinely considered a hard problem in several mathematical disciplines. In statistics this problem arises for instance in…

Statistics Theory · Mathematics 2024-08-16 Bruno Ebner , María Dolores Jiménez-Gamero , Bojana Milošević

In this paper, we present a method for the computation of the low-lying real eigenvalues of the Wilson-Dirac operator based on the Arnoldi algorithm. These eigenvalues contain information about several observables. We used them to calculate…

High Energy Physics - Lattice · Physics 2015-05-27 G. Bergner , J. Wuilloud

We summarize recent analytical results obtained for lattice artifacts of the non-Hermitian Wilson Dirac operator. Hereby we discuss the effect of all three low energy constants. In particular we study the limit of small lattice spacing and…

High Energy Physics - Lattice · Physics 2013-10-28 Mario Kieburg , Jacobus J. M. Verbaarschot , Savvas Zafeiropoulos

We apply different types of overlap operators in quenched QCD simulations to compute the zero mode contribution to the pseudo-scalar correlator. In particular we use the conventional Neuberger Dirac operator and the overlap hypercube Dirac…

High Energy Physics - Lattice · Physics 2007-05-23 S. Shcheredin , W. Bietenholz

We investigate and compute spectral sums of the Wilson lattice Dirac operator for quenched SU(3) gauge theory. It is demonstrated that there exist sums which serve as order parameters for the confinement-deconfinement phase transition and…

High Energy Physics - Lattice · Physics 2008-11-26 Franziska Synatschke , Andreas Wipf , Christian Wozar

We study correlation functions of Wilson loops and local operators in a subsector of N=4 SYM which preserves two supercharges. Localization arguments allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills theory. In…

High Energy Physics - Theory · Physics 2015-06-05 Simone Giombi , Vasily Pestun

Under various elliptic boundary conditions, we obtain lower eigenvalue estimates for Dirac operators by using Hormander's weighted $L^2$-technique. Lower bounds in terms of the volume of the underlying manifolds are also deduced from the…

Differential Geometry · Mathematics 2019-07-16 Qingchun Ji , Li Lin

In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.

Differential Geometry · Mathematics 2018-10-18 Qun Chen , Linlin Sun

We calculate the low-lying eigenvalues and eigenvectors of the hermitian domain wall Dirac operator on various gauge backgrounds by Ritz minimization. The mass dependence of these eigenvalues is studied to extract the physical 4 dimensional…

High Energy Physics - Lattice · Physics 2007-05-23 Guofeng Liu

We examine artifacts associated with the chiral symmetry breaking induced through the use of Wilson-Dirac fermions in lattice Monte Carlo computations. For light quark masses, the conventional quenched theory can not be defined using direct…

High Energy Physics - Lattice · Physics 2009-10-31 W. Bardeen , A. Duncan , E. Eichten , H. Thacker

We compute the low lying eigenvalues of the Hermitian Dirac operator in lattice QCD with $N_{\rm f} = 2+1+1$ twisted mass fermions. We discuss whether these eigenvalues are in the $\epsilon$-regime or the $p$-regime of Wilson chiral…

High Energy Physics - Lattice · Physics 2018-11-29 Krzysztof Cichy , Savvas Zafeiropoulos

In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in…

Differential Geometry · Mathematics 2018-10-09 Yongfa Chen

We investigate the effects of low-lying fermion modes on the QCD partition function in the epsilon-regime. With the overlap Dirac operator we calculate several tens of low-lying fermion eigenvalues on the quenched lattice. By partially…

High Energy Physics - Lattice · Physics 2009-11-10 Kenji Ogawa , Shoji Hashimoto

We consider properties of zero and near-zero modes for overlap fermion operator in SU(2) lattice gluodynamics. The density of the states is of the order of Lambda(QCD) while the localization volume of the modes tends to zero in physical…

High Energy Physics - Lattice · Physics 2007-05-23 M. I. Polikarpov , F. V. Gubarev , S. M. Morozov , V. I. Zakharov

The microscopic spectral density of the Hermitian Wilson-Dirac operator is computed numerically in quenched lattice QCD. We demonstrate that the results given for fixed index of the Wilson-Dirac operator can be matched by the predictions…

High Energy Physics - Lattice · Physics 2013-05-30 P. H. Damgaard , U. M. Heller , K. Splittorff

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and…

Differential Geometry · Mathematics 2009-11-13 Daniel Maerten

We investigate the properties of domain wall fermions on a set of quenched configurations at non-zero temperature. In particular, we compute the low lying eigenvalues of the DWF operator and study their relation with topology, level…

High Energy Physics - Lattice · Physics 2014-11-17 J. -F. Lagae , D. K. Sinclair

We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of…

Analysis of PDEs · Mathematics 2025-08-25 Nathanaël Boutillon