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Related papers: The overlap operator as a continued fraction

200 papers

We present simulation results for the 2-flavour Schwinger model with dynamical Ginsparg-Wilson fermions. Our Dirac operator is constructed by inserting an approximately chiral hypercube operator into the overlap formula, which yields the…

High Energy Physics - Lattice · Physics 2008-11-26 Jan Volkholz , Wolfgang Bietenholz , Stanislav Shcheredin

We construct an $O(a^2)$-improved overlap-Dirac operator by designing an improved overlap kernel, based on the Symanzik improvement program. Field rotation terms are also identified to improve off-shell amplitudes for both massless and…

High Energy Physics - Lattice · Physics 2010-11-05 H. Ikeda , S. Hashimoto

In this paper we show how to construct a Dirac operator on a lattice in complete analogy with the continuum. In fact we consider a more general problem, that is, the Dirac operator over an abelian finite group (for which a lattice is a…

High Energy Physics - Theory · Physics 2012-08-27 Jayme Vaz,

We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the…

High Energy Physics - Lattice · Physics 2013-11-20 H. Fukaya , S. Aoki , G. Cossu , S. Hashimoto , T. Kaneko , J. Noaki

The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and…

High Energy Physics - Theory · Physics 2009-10-31 Hiroshi Suzuki

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 provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined…

High Energy Physics - Lattice · Physics 2026-02-27 Shoto Aoki , Hajime Fujita , Hidenori Fukaya , Mikio Furuta , Shinichiroh Matsuo , Tetsuya Onogi , Satoshi Yamaguchi

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

We discuss the usage and applicability of deflation methods for the overlap lattice Dirac operator, focussing on calculating the eigenvalues using a method similar to the eigCG algorithm used for other Dirac operators. The overlap operator,…

High Energy Physics - Lattice · Physics 2016-05-04 Nigel Cundy , Weonjong Lee

We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive…

Numerical Analysis · Mathematics 2025-08-21 Liam Burke , Andreas Frommer , Gustavo Ramirez-Hidalgo , Kirk M. Soodhalter

We discuss the adaptation of the Hybrid Monte Carlo algorithm to overlap fermions. We derive a method which can be used to account for the delta function in the fermionic force caused by the differential of the sign function. We discuss the…

High Energy Physics - Lattice · Physics 2009-11-11 Nigel Cundy

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

According to the necessary requirements for a chirally symmetric Dirac operator, we present a systematic construction of such operators. We formulate a criterion for the hermitian operator which enters the construction such that the doubled…

High Energy Physics - Lattice · Physics 2011-02-16 Ting-Wai Chiu

In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is…

Spectral Theory · Mathematics 2023-05-23 Feng Wang , Chuan-Fu Yang

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

We discuss the salient features of Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with overlap Dirac quark. The theoretical error bound for the matrix-vector…

High Energy Physics - Lattice · Physics 2011-02-16 Ting-Wai Chiu , Tung-Han Hsieh , Chao-Hsi Huang , Tsung-Ren Huang

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a…

High Energy Physics - Lattice · Physics 2009-11-07 David H. Adams

I review the lattice formulations of vector-like gauge theories (e.g. QCD) with domain-wall/overlap fermions, and discuss how to optimize the chiral symmetry for any finite $ N_s $ (sites in the fifth dimension). In this formulation, quark…

High Energy Physics - Lattice · Physics 2011-02-16 Ting-Wai Chiu

I apply a recently developed algorithm for reweighting simulations of lattice QCD from one quark mass to another to simulations performed with overlap fermions in the epsilon regime. I test it by computing the condensate from distributions…

High Energy Physics - Lattice · Physics 2009-01-08 Thomas DeGrand

Renormalizability of a lattice chiral fermion is studied at one loop level in the overlap formulation in four dimensions. The fermion chirality is examined including the self-energy corrections due to gauge interactions. Divergent terms…

High Energy Physics - Lattice · Physics 2009-10-30 Atsushi Yamada