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Related papers: The overlap operator as a continued fraction

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In this paper I propose the use of a lattice derivative operator that is equivalent to the ideal SLAC derivative operator in all lattice calculations, but without the prohibitively expensive computational cost of the latter. A pedagogical…

High Energy Physics - Lattice · Physics 2007-05-23 John P. Costella

An alternative to commonly used domain wall fermions is presented. Some rigorous bounds on the condition number of the associated linear problem are derived. On the basis of these bounds and some experimentation it is argued that domain…

High Energy Physics - Lattice · Physics 2009-11-07 H. Neuberger

Evaluation of the continuum limit of the axial anomaly and index is sketched for the staggered overlap Dirac operator. There are new complications compared to the usual overlap case due to the distribution of the spin and flavor components…

High Energy Physics - Lattice · Physics 2013-12-30 David H. Adams , Reetabrata Har , Yiyang Jia , Christian Zielinski

In this proceeding we propose a new procedure to impose the Schroedinger functional Dirichlet boundary condition on the overlap Dirac operator and the domain-wall fermion using an orbifolding projection. With this procedure the zero mode…

High Energy Physics - Lattice · Physics 2016-09-01 Yusuke Taniguchi

The overlap fermion offers the considerable advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given…

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…

High Energy Physics - Theory · Physics 2021-12-22 Dominik Ciurla , Leszek Hadasz , Thomas Williams

We compute the ratio $\Lambda_L/\Lambda_{\bar{MS}}$ between the scale parameter $\Lambda_L$, associated with a lattice formulation of QCD using the overlap-Dirac operator, and $\Lambda_{\bar{MS}}$ of the $\bar{\rm MS}$ renormalization…

High Energy Physics - Lattice · Physics 2009-10-31 C. Alexandrou , H. Panagopoulos , E. Vicari

The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at…

High Energy Physics - Lattice · Physics 2009-11-10 S. Shcheredin , W. Bietenholz , T. Chiarappa , K. Jansen , K. -I. Nagai

Taking into account of the boundary condition in the fifth direction which is derived from the lattice Wilson fermion, we develop a theory of five-dimensional fermion with kink-like and homogeneous masses in finite extent of the fifth…

High Energy Physics - Lattice · Physics 2016-08-31 T. Kawano , Y. Kikukawa

In odd dimensions the lattice overlap formalism is simpler than in even dimensions. Masslessness of fermions can still be preserved without fine tuning and gauge invariance without gauge averaging can be maintained, although, sometimes,…

High Energy Physics - Lattice · Physics 2009-10-30 Y. Kikukawa , H. Neuberger

We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…

High Energy Physics - Theory · Physics 2009-11-10 A. Kirchberg , J. D. Laenge , A. Wipf

Computing the trace of the inverse of large matrices is typically addressed through statistical methods. Deflating out the lowest eigenvectors or singular vectors of the matrix reduces the variance of the trace estimator. This work…

Numerical Analysis · Mathematics 2020-03-18 Eloy Romero , Andreas Stathopoulos , Kostas Orginos

We propose and study a generalized continued fraction algorithm that can be executed in an arbitrary imaginary quadratic field, the novelty being a non-restriction to the five Euclidean cases. Many hallmark properties of classical continued…

Number Theory · Mathematics 2022-07-12 Daniel E. Martin

We compute non-perturbatively the renormalization constants of composite operators for overlap fermions by using the regularization independent scheme. The scaling behavior of the renormalization constants is investigated using the data…

High Energy Physics - Lattice · Physics 2007-05-23 J. B. Zhang , D. B. Leinweber , A. G. Williams

As shown in earlier work, skew-adjoint linear differential operators, mapping efforts into flows, give rise to Dirac structures on a bounded spatial domain by a proper definition of boundary variables. In the present paper this is extended…

Optimization and Control · Mathematics 2021-05-05 Arjan van der Schaft , Bernhard Maschke

In this paper, we introduce the overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, to the matter sector of two-dimensional N=(2,2) lattice supersymmetric QCD (SQCD) with preserving one of the supercharges. It realizes the…

High Energy Physics - Lattice · Physics 2009-11-19 Yoshio Kikukawa , Fumihiko Sugino

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An…

High Energy Physics - Lattice · Physics 2009-11-07 H. Kurokawa , T. Fujiwara

In this work we consider a class of delay eigenvalue problems that admit a spectrum similar to that of a Hamiltonian matrix, in the sense that the spectrum is symmetric with respect to both the real and imaginary axis. More precisely, we…

Numerical Analysis · Mathematics 2022-07-15 Pieter Appeltans , Wim Michiels

The overlap operator provides an elegant definition for the winding number of lattice gauge field configurations. Only for a set of configurations of measure zero is this procedure undefined. Without restrictions on the lattice fields,…

High Energy Physics - Lattice · Physics 2009-11-07 Michael Creutz

The eigenvalue spectrum $\rho(\lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract…

High Energy Physics - Lattice · Physics 2018-07-11 Katsumasa Nakayama , Hidenori Fukaya , Shoji Hashimoto