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Related papers: The overlap Dirac operator as a continued fraction

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I show how to avoid a two level nested conjugate gradient procedure in the context of Hybrid Monte Carlo with the overlap fermionic action. The resulting procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but is…

High Energy Physics - Lattice · Physics 2016-08-25 Herbert Neuberger

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…

High Energy Physics - Lattice · Physics 2009-11-10 Nigel Cundy , Andreas Frommer , Jasper van den Eshof , Thomas Lippert , Stephan Krieg , Katrin Schäfer

The Overlap operator fulfills the Ginsparg-Wilson relation exactly and therefore represents an optimal discretization of the QCD Dirac operator with respect to chiral symmetry. When computing propagators or in HMC simulations, where one has…

High Energy Physics - Lattice · Physics 2011-12-16 Andreas Frommer , Karsten Kahl , Thomas Lippert , H. Rittich

We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…

Spectral Theory · Mathematics 2022-06-28 Sergey Buterin , Nebojša Djurić

The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be…

High Energy Physics - Lattice · Physics 2008-11-26 Rajamani Narayanan

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…

High Energy Physics - Lattice · Physics 2009-07-09 H. Neuberger

We describe an explicit construction of approximate Ginsparg-Wilson fermions for QCD. We use ingredients of perfect action origin, and further elements. The spectrum of the lattice Dirac operator reveals the quality of the approximation. We…

High Energy Physics - Lattice · Physics 2009-10-31 W. Bietenholz , N. Eicker , I. Hip , K. Schilling

We show the result of the lattice gauge field tensor which is derived from the classical continuum limit of the overlap Dirac operator. By analogous construction, it was recently proposed that the gauge action can be obtained from the…

High Energy Physics - Lattice · Physics 2009-04-14 K. F. Liu

The overlap lattice-Dirac operator contains the sign function $\epsilon (H)$. Recent practical implementations replace $\epsilon (H)$ by a ratio of polynomials, $H P_n (H^2)/Q_n (H^2)$, and require storage of $2n+2$ large vectors. Here I…

High Energy Physics - Lattice · Physics 2015-06-25 Herbert Neuberger

Numerical evaluation of the overlap Dirac operator is difficult since it contains the sign function $\epsilon(H_w)$ of the Hermitian Wilson-Dirac operator $H_w$ with a negative mass term. The problems are due to $H_w$ having very small…

High Energy Physics - Lattice · Physics 2016-09-01 W. Kamleh , D. Adams , D. B. Leinweber , A. G. Williams

On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate…

High Energy Physics - Lattice · Physics 2009-09-29 Hiroto So , Masashi Hayakawa , Hiroshi Suzuki

The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix-vector product that involves the sign function of the hermitian Wilson matrix. In this paper we…

High Energy Physics - Lattice · Physics 2009-11-07 J. van den Eshof , A. Frommer , Th. Lippert , K. Schilling , H. A. van der Vorst

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…

High Energy Physics - Lattice · Physics 2015-06-25 C. Alexandrou , E. Follana , H. Panagopoulos , E. Vicari

In the continuum, a topological obstruction to the vanishing of the non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac…

High Energy Physics - Lattice · Physics 2008-11-26 David H. Adams

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

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 prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in…

Spectral Theory · Mathematics 2016-09-01 Yuri A. Ashrafyan , Tigran N. Harutyunyan

We compute Neuberger's overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied.

High Energy Physics - Lattice · Physics 2011-07-19 Artan Borici

We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that…

Dynamical Systems · Mathematics 2024-01-09 Boris Solomyak

Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…

Quantum Physics · Physics 2013-07-16 Jeffrey Yepez